- A
- B
- C
- D
Step-by-Step Solution
Split the pentagon: rectangle = ; triangle = ½ × . Total = . Trap : forgetting the ½ on the triangle (360 + 240). Trap : halving the triangle twice (360 + 60). Trap : the rectangle alone, leaving the tip out.
Answer: C)
A park is shaped like a pentagon: a rectangle 24 m long and 15 m wide, with a triangular tip of base 24 m and height 10 m sitting on one of the 24 m sides. Find the total area of the park.
Class 8MensurationMensuration
Key idea: Area of a trapezium
**Area of a trapezium = ½ × (sum of parallel sides) × height.**
The height is the **perpendicular distance** between the two parallel sides — NOT the slant length of the non-parallel side.
Example: parallel sides 8 cm and 5 cm, height 4 cm. Area = ½ × = ½ × .
Why ½? You can split a trapezium into a rectangle plus a triangle (or chop and rearrange into a rectangle of the average parallel side). The factor of ½ comes from averaging the two parallel sides.
The height is the **perpendicular distance** between the two parallel sides — NOT the slant length of the non-parallel side.
Example: parallel sides 8 cm and 5 cm, height 4 cm. Area = ½ × = ½ × .
Why ½? You can split a trapezium into a rectangle plus a triangle (or chop and rearrange into a rectangle of the average parallel side). The factor of ½ comes from averaging the two parallel sides.
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