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Compound Shape Areas
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Compound Shape Areas
Break each compound shape into familiar shapes, find their areas, and combine the results. Show your working and include square units.
Build the method
Use rectangle area = length × width and triangle area = ½ × base × perpendicular height.
1.A builder splits a compound shape into a rectangle measuring 9 cm by 4 cm and a rectangle measuring 3 cm by 2 cm. What is the total area?
2.A rectangle measuring 10 m by 6 m has a 4 m by 2 m rectangular notch cut out of it. Calculate the remaining area.
3.A sign consists of a rectangle 12 cm wide and 5 cm high, with a triangle on top. The triangle has a base of 12 cm and a perpendicular height of 4 cm. Find the sign’s area.
4.Which expression gives the area of a compound shape made from a 7 cm × 5 cm rectangle and a triangle with base 7 cm and perpendicular height 3 cm?
- 7 × 5 + ½ × 7 × 3
- 7 + 5 + 7 + 3
- 7 × 5 × 7 × 3
- 7 × 5 − ½ × 7 × 3
5.A compound floor has area 72 m². One part is a rectangle measuring 8 m by 6 m; the other part is a triangle with base 6 m. What is the triangle’s perpendicular height?
6.A student finds the areas of two rectangles, 8 cm × 3 cm and 5 cm × 4 cm, then writes the compound area as 24 + 20 = 44 cm. Identify the mistake and give the corrected answer.
7.A rectangular patio measures 11 m by 7 m. A triangular flower bed attached along one 7 m side has perpendicular height 3 m. How much area is there altogether?
8.Design a compound shape using exactly three rectangles. Label each rectangle’s length and width, then calculate the total area. Make sure the rectangles join without overlapping.
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