Answer:
height ≈ 5.70 m
Base ≈ 13.70 m
Area = 61.845 m
Step-by-step explanation:
The figure above is a trapezium. The area of a trapezium is given as
1/2 × (a + b) × h
a = 8m
b = ?
using the right angle triangle we can find the height and the base .
Applying SOHCAHTOA principle
sin 45° = opposite/hypotenuse
sin 45° = opposite/8
cross multiply
opposite = 8 × sin 45°
opposite = 8 × 0.7071067812
opposite = 5.6568542495
height = 5.70 m
Base of the triangle
cos 45° = adjacent/hypotenuse
0.7071067812 = adjacent/ 8
adjacent = 8 × 0.7071067812
adjacent = 5.6568542495
adjacent = 5. 70 m
area of trapezium = 1/2 × (a + b) × h
a = 8 m
b = 5.7 + 8 = 13.7 cm
h = 5.7 cm
area of trapezium = 1/2 × (8 + 13.7) × 5.7
area of trapezium = 1/2 × 21.7 × 5.7
area of trapezium = 1/2 × 123.69
area of trapezium = 61.845 m
