Question

What is the area of the trapezoid to the nearest tenth? 62.4 ft2 41.9 ft2 65.0 ft2 76.7 ft2

Answer 1

Find height:


`\boxed {\boxed { \sin(\theta) = \frac{\text{opp}}{\text{hyp}} }}`


`\sin(60) = \frac{\text{opp}}{8}}`


`\text{opp} = 8\sin(60)`


`\text{opp} = 6.93 \text{ ft}`

Height = 6.93

Find missing base length:


`\boxed { \boxed { \cos(\theta) = \frac{\text{adj}}{\text{hyp}} }}`


`\cos(60) = \frac{\text{adj}}{8}}`


`\text{adj} = 8\cos(60)`


`\text{adj} = 4 \text{ ft}`

Base length = 7 + 4 = 11 ft

Find area:


`\boxed {\boxed { \text {Area of trapezium = } (1)/(2) (a + b)h}}`


`\text {Area of trapezium = } (1)/(2) (11 +7)(6.93)`


`\text {Area of trapezium = } 62.4 \text{ ft. (nearest tenth)}`