Podcast
Questions and Answers
In a parallelogram, if the base is doubled and the height is halved, how does the area change?
In a parallelogram, if the base is doubled and the height is halved, how does the area change?
- The area remains the same. (correct)
- The area is doubled.
- The area becomes four times.
- The area is halved.
The area of a parallelogram is always greater than the area of a rectangle with the same perimeter.
The area of a parallelogram is always greater than the area of a rectangle with the same perimeter.
False (B)
A parallelogram has adjacent sides of lengths 8 cm and 12 cm. If the height corresponding to the side of length 12 cm is 6 cm, what is the height corresponding to the side of length 8 cm?
A parallelogram has adjacent sides of lengths 8 cm and 12 cm. If the height corresponding to the side of length 12 cm is 6 cm, what is the height corresponding to the side of length 8 cm?
9 cm
If the area of a parallelogram is $48 cm^2$ and its height is 6 cm, then its base is ________ cm.
If the area of a parallelogram is $48 cm^2$ and its height is 6 cm, then its base is ________ cm.
Match each geometric term with its correct formula:
Match each geometric term with its correct formula:
In a triangle, if the base is increased by 20% and the height is decreased by 20%, what is the percentage change in the area?
In a triangle, if the base is increased by 20% and the height is decreased by 20%, what is the percentage change in the area?
If two triangles have the same base and lie between the same parallel lines, then they are congruent.
If two triangles have the same base and lie between the same parallel lines, then they are congruent.
If a triangle has an area of $36 cm^2$ and a base of 12 cm, what is its corresponding height?
If a triangle has an area of $36 cm^2$ and a base of 12 cm, what is its corresponding height?
If the area of an equilateral triangle is $16\sqrt{3}$ $cm^2$, then the length of each of its sides is ________ cm.
If the area of an equilateral triangle is $16\sqrt{3}$ $cm^2$, then the length of each of its sides is ________ cm.
Match the type of triangle with its area calculation requirement:
Match the type of triangle with its area calculation requirement:
A wire is bent in the form of a circle of radius 28 cm. If it is rebent into a square, what is the area of the square?
A wire is bent in the form of a circle of radius 28 cm. If it is rebent into a square, what is the area of the square?
Increasing the radius of a circle by 50% will increase its area by 125%.
Increasing the radius of a circle by 50% will increase its area by 125%.
The circumference of a circle is $88$ cm. Find its area.
The circumference of a circle is $88$ cm. Find its area.
If the area of a circle is $49Ï€$ $cm^2$, then its diameter is ________ cm.
If the area of a circle is $49Ï€$ $cm^2$, then its diameter is ________ cm.
Match the part of the circle with its respective formula:
Match the part of the circle with its respective formula:
A square is inscribed in a circle. If the side of the square is 'a', what is the area of the circle?
A square is inscribed in a circle. If the side of the square is 'a', what is the area of the circle?
The ratio of the circumference of a circle to its diameter is a rational number.
The ratio of the circumference of a circle to its diameter is a rational number.
If the circumference of a circle is numerically equal to its area, what is its radius?
If the circumference of a circle is numerically equal to its area, what is its radius?
If the area of a semicircle is $8Ï€$ $cm^2$, then the radius of the circle is ________ cm.
If the area of a semicircle is $8Ï€$ $cm^2$, then the radius of the circle is ________ cm.
Match the descriptions with the correct components of a circle:
Match the descriptions with the correct components of a circle:
Flashcards
Area of a Parallelogram
Area of a Parallelogram
The amount of surface a parallelogram covers.
Base of a Parallelogram
Base of a Parallelogram
Any side of a parallelogram.
Height of a Parallelogram
Height of a Parallelogram
The perpendicular distance from the base to the opposite vertex.
Area of a Triangle
Area of a Triangle
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Circumference
Circumference
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Pi (Ï€)
Pi (Ï€)
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Diameter
Diameter
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Radius
Radius
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Area of a Circle
Area of a Circle
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Study Notes
- Chapter 9 focuses on perimeter and area calculation.
Area of a Parallelogram
- Parallelograms can be converted into rectangles of equal area.
- To find a parallelogram's area, cut it out on graph paper, draw a perpendicular line from one vertex to the opposite side, and move the resulting triangle to the other side. This forms a rectangle.
- Parallelogram area equals the area of the rectangle formed after the transformation.
- The length and breadth of the rectangle correspond to the base and height of the parallelogram.
- The area of a parallelogram = base × height = b × h
- Any side of a parallelogram can be considered its base.
- Height (or altitude) is the perpendicular distance from the opposite vertex to the base.
- To calculate the area by counting squares enclosed figures and measure sides
- Parallelograms with equal areas can have different perimeters
- Different areas are possible with parallelograms of equal perimeters.
- Knowing the base and corresponding height is needed to find an area
Area of a Triangle
- Two identical scalene triangles can form a parallelogram when corresponding sides are joined.
- The combined area of two identical triangles equals the area of the parallelogram they form.
- The base and height of the triangle correspond to the base and height of the parallelogram.
Area of each triangle = 1/2 (Area of parallelogram)- A triangle's area is calculated as 1/2 × base × height, or (1/2)bh.
- For an obtuse-angled triangle, the height may fall outside the triangle.
Circumference of a Circle
- The distance around a circular region is the circumference.
- Circumference is determined by marking and rolling circular shape along the ruler
- The ratio of circumference to diameter is constant.
- Pi (Ï€) is used to denote a constant ratio
- π is approximately 22/7 or 3.14.
C/d = π,C = πd- Circle diameter (d) is twice the radius (r), or
d = 2r C = π x 2rorC = 2πr
Area of a Circle
- Dividing a circle into sectors and rearranging them forms a rectangle.
- The breadth of the rectangle is equal to the circle's radius.
- Circle area is calculated as πr².
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