Geometry: Area and Perimeter

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Questions and Answers

What is the formula for the area of a parallelogram?

  • Base × Height (correct)
  • Length + Breadth
  • Length × Height
  • Base + Height

The area of a parallelogram is equal to the area of a rectangle formed when it is split along its height.

True (A)

What do you call the perpendicular line dropped from a vertex to the opposite side in a parallelogram?

Height (or altitude)

The area of a parallelogram is calculated as the product of its base and _____ .

<p>height</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Base = The bottom side of the parallelogram. Height = The perpendicular distance from the base to the opposite vertex. Parallelogram = A four-sided figure with opposite sides parallel. Area = The extent of a two-dimensional surface within a boundary.</p> Signup and view all the answers

If the base of a parallelogram is 10 cm and its height is 5 cm, what is its area?

<p>50 cm² (A)</p> Signup and view all the answers

Any side of a parallelogram can be chosen as the base for calculating the area.

<p>True (A)</p> Signup and view all the answers

Describe how a parallelogram can be transformed into a rectangle.

<p>By cutting a triangle from one side and moving it to the opposite side, a rectangle can be formed.</p> Signup and view all the answers

What is the formula for the area of a triangle in relation to the area of a parallelogram?

<p>Area = (base × height) / 2 (D)</p> Signup and view all the answers

The height of a triangle is always located inside the triangle itself.

<p>False (B)</p> Signup and view all the answers

If the base of a parallelogram is 6 cm and its height is 4 cm, what is the area of the parallelogram?

<p>24 cm²</p> Signup and view all the answers

The area of a parallelogram is equal to the product of its base and ______.

<p>height</p> Signup and view all the answers

Match the triangle types with their properties:

<p>Equilateral Triangle = All sides and angles are equal Isosceles Triangle = Two sides are of equal length Scalene Triangle = All sides are of different lengths Obtuse Triangle = One angle is greater than 90 degrees</p> Signup and view all the answers

Which of the following statements about congruent triangles is correct?

<p>Congruent triangles must be equal in shape and size. (B)</p> Signup and view all the answers

Two triangles can have the same area but still be congruent.

<p>False (B)</p> Signup and view all the answers

What can be said about the triangles formed by cutting a parallelogram along its diagonals?

<p>The triangles are congruent.</p> Signup and view all the answers

What is the perimeter of each semicircular shape disc with a radius of 7 cm?

<p>36 cm (C)</p> Signup and view all the answers

The circumference of a circle is always greater than its diameter.

<p>True (A)</p> Signup and view all the answers

What is the diameter of a circle with a radius of 7 cm?

<p>14 cm</p> Signup and view all the answers

The circumference of a semicircle with a radius of 7 cm is _____ cm.

<p>22</p> Signup and view all the answers

Match the term to its corresponding value:

<p>Radius = 7 cm Diameter = 14 cm Circumference of semicircle = 22 cm Perimeter of semicircular disc = 36 cm</p> Signup and view all the answers

What formula is used to calculate the circumference of a semicircle?

<p>$ rac{1}{2} imes 2 ext{Ï€}r$ (D)</p> Signup and view all the answers

The total perimeter of the given figure is 88 cm.

<p>True (A)</p> Signup and view all the answers

If a farmer wants to cover an area with radius 7 m, how many kilograms of fertiliser does he need?

<p>49 kg</p> Signup and view all the answers

What is the formula for the area of a circle?

<p>$ ext{Area} = rac{22}{7}r^2$ (D)</p> Signup and view all the answers

The circumference of a circle is calculated using the formula $2Ï€r$.

<p>True (A)</p> Signup and view all the answers

What is the area of a circular table-top with a radius of 2 m at the rate of ₹10 per square meter?

<p>₹40</p> Signup and view all the answers

The area of a circle can be found by using the formula __________.

<p>$Ï€r^2$</p> Signup and view all the answers

Match the following shapes to their calculations:

<p>Circle = πr² Square = s² Rectangle = l × b Triangle = ½ × base × height</p> Signup and view all the answers

If the radius of a circle is doubled, how does the area change?

<p>It quadruples (C)</p> Signup and view all the answers

The diameter of a circle is twice the radius.

<p>True (A)</p> Signup and view all the answers

What is the area of a circular garden with a diameter of 9.8 m?

<p>75.28 m²</p> Signup and view all the answers

What is the formula to find the area of a parallelogram?

<p>Base × Height (C)</p> Signup and view all the answers

The area of triangle with base 8 cm and height 5 cm is 20 cm².

<p>False (B)</p> Signup and view all the answers

What is the height of a triangle if the base is 10 cm and the area is 50 cm²?

<p>10 cm</p> Signup and view all the answers

The area of a parallelogram with a base of _____ cm and a height of 6 cm is 84 cm².

<p>14</p> Signup and view all the answers

Given that the area of parallelogram PQRS is calculated with height QM = 7.6 cm and base SR = 12 cm, what is the area?

<p>91.2 cm² (B)</p> Signup and view all the answers

The area of triangle ABC is equal to 30 cm² when the base is 15 cm and the height is 4 cm.

<p>True (A)</p> Signup and view all the answers

The area of triangle with a base of 22 cm and height of _____ cm is 170.5 cm².

<p>15.5</p> Signup and view all the answers

What is the area of the larger circle with a radius of 10 cm?

<p>314 cm² (D)</p> Signup and view all the answers

The radius of the smaller circle in the example is 3 cm.

<p>False (B)</p> Signup and view all the answers

Calculate the area of a circle with a diameter of 49 m using π = 3.14.

<p>1924.86 m²</p> Signup and view all the answers

The area of the shaded region between the two circles is ___ cm².

<p>263.76</p> Signup and view all the answers

Match the following circles with their respective areas:

<p>Circle A (radius 10 cm) = 314 cm² Circle B (radius 4 cm) = 50.24 cm² Circle C (radius 3 cm) = 28.26 cm² Circle D (radius 5 cm) = 78.5 cm²</p> Signup and view all the answers

If the circumference of a circular sheet is 154 m, what is its radius? (Take π = 22/7)

<p>21 m (C)</p> Signup and view all the answers

To fence a circular garden of diameter 21 m, the gardener needs a rope of 22 m.

<p>False (B)</p> Signup and view all the answers

What is the area of a circle with a radius of 14 mm using π = 22/7?

<p>615.75 mm²</p> Signup and view all the answers

Flashcards

Parallelogram

A four-sided shape with opposite sides parallel.

Base of a Parallelogram

The length of the base of a parallelogram.

Height of a Parallelogram

The perpendicular distance from the base to the opposite side of a parallelogram.

Area of a Parallelogram

The area of a parallelogram is calculated by multiplying its base by its height.

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Choosing the Base

Any side of a parallelogram can be chosen as its base.

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Height as Perpendicular

A line segment drawn from a vertex of the parallelogram perpendicular to its base represents the height.

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Parallelogram to Rectangle

A parallelogram can be transformed into a rectangle with the same area by cutting and rearranging a triangle.

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Area Conservation

The area of a parallelogram remains unchanged even after transforming it into a rectangle.

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Parallelogram to Triangles

Dividing a parallelogram into two triangles along its diagonal results in two triangles with equal areas.

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Triangle Area

The area of a triangle is half the area of a parallelogram with the same base and height.

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Equal Area, Different Shapes

Triangles with equal area don't necessarily have the same shape.

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Triangle Height

The height of a triangle is the perpendicular distance from the vertex to the base.

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Triangle Area Formula

The formula for finding the area of a triangle is (1/2) * base * height.

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Triangle Base

The base of a triangle can be any side of the triangle.

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Congruent vs. Equal Area

Congruent triangles have the same shape and size, while triangles with equal area can have different shapes.

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Choosing the Base of a Parallelogram

Any side of a parallelogram can be chosen as its base, and the corresponding altitude (height) is then drawn perpendicular to that base.

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Area of a Triangle

The area of a triangle is half the product of its base and its height.

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Height of a Triangle

The perpendicular distance from a vertex of a triangle to its base.

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Base of a Triangle

The side of a triangle to which the altitude (height) is drawn.

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Height as Perpendicular (Triangle)

A line segment drawn from a vertex of the triangle perpendicular to its base represents the height.

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Circumference of a Circle

The distance around a circle, calculated by multiplying the diameter by pi.

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Circumference of a Semicircle

Half the circumference of a circle, calculated by dividing the circle's circumference by 2.

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Perimeter

The total length of all the sides of a shape.

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Diameter of a Circle

The distance across a circle through its center.

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Radius of a Circle

The distance from the center of a circle to a point on its edge.

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Area

The area of a closed shape, representing the amount of space it occupies.

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Area of a Circle

The area of a circle is found by multiplying Pi by the square of the radius.

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Semicircle

A section of a circle that is bounded by a diameter and an arc.

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Pi (Ï€)

The ratio of a circle's circumference to its diameter, approximately equal to 3.14.

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Rectangle

A shape with four straight sides and four right angles, where opposite sides are equal.

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Length (l)

The length of one side of a rectangle.

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Circumference Formula

The formula for calculating the circumference of a circle is C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius.

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Area Formula

The formula for calculating the area of a circle is A = πr², where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius.

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Diameter and Radius Relationship

The relationship between diameter (d) and radius (r) of a circle is d = 2r, meaning the diameter is twice the length of the radius.

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Finding the Radius for Area Calculation

To efficiently find the area of a circle, you need to know the radius. If the diameter is given, you can easily calculate the radius by dividing the diameter by 2.

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Study Notes

Perimeter and Area

  • Parallelograms can be transformed into rectangles of equal area.
  • Area of a parallelogram = base × height
  • The base of a parallelogram can be any side.
  • The height of a parallelogram is the perpendicular distance from the base to the opposite side.
  • Area of a triangle = (1/2) × base × height

Area of a Triangle

  • Triangles can be combined to form a parallelogram.
  • Area of a triangle is half the area of the parallelogram.
  • The base of a triangle can be any side.
  • The height of a triangle is the perpendicular distance from the base to the opposite vertex.

Circumference of a Circle

  • The distance around a circular region is called the circumference.
  • Circumference = Ï€ × diameter (where Ï€ is approximately 3.14)
  • Circumference = 2 × Ï€ × radius
  • The ratio of circumference to diameter of a circle is a constant (Ï€).

Area of a Circle

  • The area of a circle is the amount of space enclosed within the circle edges
  • Area = Ï€ × radius × radius (where Ï€ is approximately 3.14)

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