Question

9. Determine the area of the figure below.
5.5 cm
8 cm
12 cm
6.8 cm

Answer 1

Area of the given figure would be :

" Sum of area of Trapezoid and Semicircle "

Lets calculate the area of Trapezoid first ~

its " 1/2 times (sum of parallel sides) times (perpendicular distance between them) "

`\qquad\displaystyle \tt \dashrightarrow \: (1)/(2) * ( 8+ 12) * (5.5)`

`\qquad\displaystyle \tt \dashrightarrow \: (1)/(2) * (20) * (5.5)`

`\qquad\displaystyle \tt \dashrightarrow \: 10 * 5.5`

`\qquad\displaystyle \tt \dashrightarrow \: 55 \: \: cm {}^(2)`

Next, area of Semicircle ~

`\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi {r}^(2) }{2}`

`\textsf{[ diameter (d) = 8 cm, radius (r) = d/2 = 8/2 = 4 cm ]}`

`\qquad\displaystyle \tt \dashrightarrow \: \frac{3.14 * ( {4)}^(2) }{2}`

`\qquad\displaystyle \tt \dashrightarrow \: 1.57 * 16`

`\qquad\displaystyle \tt \dashrightarrow \: 25.12 \: \: cm {}^(2)`

Now, Area of the composite figure :

- Area of Trapezoid + Area of Semicircle

`\qquad\displaystyle \tt \dashrightarrow \: 55 + 25.12 = 80.12 \: cm²`