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Questions and Answers
A rectangular garden has a length of 20 meters and a width of 15 meters. A square garden has sides of 18 meters. Which garden has a larger area and by how much?
A rectangular garden has a length of 20 meters and a width of 15 meters. A square garden has sides of 18 meters. Which garden has a larger area and by how much?
- The rectangular garden is larger by 6 square meters.
- The rectangular garden is larger by 24 square meters.
- The square garden is larger by 6 square meters. (correct)
- The square garden is larger by 24 square meters.
A wire of length 60 cm is bent into a square. If the same wire is bent into a rectangle with a length of 18 cm, what is the breadth of the rectangle?
A wire of length 60 cm is bent into a square. If the same wire is bent into a rectangle with a length of 18 cm, what is the breadth of the rectangle?
- 3 cm
- 7 cm
- 15 cm
- 12 cm (correct)
What is the area of a parallelogram with a base of 15 cm and a height that is a third of its base?
What is the area of a parallelogram with a base of 15 cm and a height that is a third of its base?
- 5 cm²
- 45 cm²
- 75 cm² (correct)
- 225 cm²
A circular disc has a radius of 14 cm. What is the circumference of the disc?
A circular disc has a radius of 14 cm. What is the circumference of the disc?
If the area of a square is 64 cm², what is the length of its diagonal?
If the area of a square is 64 cm², what is the length of its diagonal?
A rectangular park is 40 m long and 30 m wide. A 2 m wide path is built inside the park along its border. Find the area of the path.
A rectangular park is 40 m long and 30 m wide. A 2 m wide path is built inside the park along its border. Find the area of the path.
The side of an equilateral triangle is 8 cm. What is its area?
The side of an equilateral triangle is 8 cm. What is its area?
A rectangle is divided into two equal triangles by drawing a diagonal. If the area of the rectangle is 72 cm², what is the area of each triangle?
A rectangle is divided into two equal triangles by drawing a diagonal. If the area of the rectangle is 72 cm², what is the area of each triangle?
If the circumference of a circle is equal to the perimeter of a square, both having a value of 88 cm, which one has a larger area?
If the circumference of a circle is equal to the perimeter of a square, both having a value of 88 cm, which one has a larger area?
A square of side 4 cm is cut out from each corner of a rectangular sheet of length 24 cm and breadth 18 cm. The sides are then folded to form a box. What is the area of the base of the box?
A square of side 4 cm is cut out from each corner of a rectangular sheet of length 24 cm and breadth 18 cm. The sides are then folded to form a box. What is the area of the base of the box?
Flashcards
Area vs. Perimeter
Area vs. Perimeter
The area of a closed figure is the part of the plane it occupies. Perimeter is the distance around it.
Area of a square
Area of a square
Side multiplied by itself (side * side).
Perimeter of a rectangle
Perimeter of a rectangle
2 * (length + breadth) is how much fencing you need.
Area of a rectangle
Area of a rectangle
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Parallelogram Area
Parallelogram Area
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Circle Circumference
Circle Circumference
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What is Pi?
What is Pi?
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Circumference formula
Circumference formula
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Area of a circle
Area of a circle
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Area Unit Conversion
Area Unit Conversion
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Study Notes
- The area of a closed figure refers to the portion of a plane it occupies, while the perimeter is the distance surrounding the figure.
- Area is measured in square meters.
Perimeter and Area of Squares and Rectangles
- Perimeter of a square = 4 × side
- Perimeter of a rectangle = 2 × (length + breadth)
- Area of a square = side × side
- Area of a rectangle = length × breadth
Example Problem: Wire Rebent from Square to Rectangle
- A wire shaped as a square with a 12 cm side is rebent into a rectangle with a 16 cm length.
- The breadth of the rectangle is 8 cm
- The square encloses more area (144 cm²) than the rectangle (128 cm²), even with the same perimeter.
Triangles as Parts of Rectangles
- A rectangle's area equals the sum of the areas of two triangles formed by its diagonal.
- The two triangles formed by the diagonal have the same area.
- Area of each triangle for a rectangle = 1/2 × length × breadth
- Area of each triangle for a square = 1/4 × (side)²
Area of a Parallelogram
- Any side can be the base.
- Height (altitude) - the perpendicular distance from the base to the opposite vertex.
- Area = Base × Height
Example: Parallelogram Area
- A parallelogram with a side of 17 cm and corresponding height of 7 cm has an area of 119 cm².
Area of a Triangle
- Area = 1/2 × Base × Height
- Area of an equilateral triangle = (√3 / 4) × (side)²
- Congruent triangles always have the same area
- Triangles with the same area are not necessarily congruent.
Circumference of a Circle
- It's the distance around the circular location.
- The ratio of a circle's circumference to its diameter is constant, denoted as π (pi).
- Circumference (C) = πd, where d is the diameter.
- Circumference (C) = π × 2r
- π is approximately 22/7 or 3.14.
Area of Circle
- Area = πr²
- r is the radius of the circle.
Conversion Of Units
- Units of area can be converted similarly to units of length.
- 1 cm² = 100 mm²
- 1 m² = 10000 cm²
- 1 hectare = 10000 m²
- Converting to a smaller unit results in a greater number of units.
- Converting to a larger unit results in a smaller number of units.
Example: Area of Path around a Rectangular Park
- A rectangular park is 55 m long and 20 m wide.
- A 3.5 m wide path surrounds the park.
- The area of the path is 574 m².
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