- A
- B
- C
- D
Step-by-Step Solution
Above AD: . Below AD: . Total .
Answer: B)
A surveyor sketched field ABCDE using the base line AD = 100 m. The dashed orange offsets to B, C and E are perpendicular to AD, and the small black numbers on AD give each foot's distance from A (all in metres). Find the area of the field.
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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