Question

Find the area of the figure. Round your answer to the nearest hundredth.

Answer 1

$\bold{\huge{\underline{ Solution }}}$

Given :-

• We have given one irregular figure which is composed of semicircle and parallelogram

To Find :-

• We have to find the total area of the given irregular figure .

Let's Begin :-

We have,

• Semicircle having diameter = 8 in.
• Therefore, R = 8/2 = 4 in.
• Parallelogram having base and height 10 in. and 6 in.

We know that,

Area of semicircle

$\bold{\pink{ = }}{\bold{\pink{\dfrac{1}{2}}}}{\bold{\pink{\pi{r^{2}}}}}$

Subsitute the required values,

$\sf{ = }{\sf{\dfrac{22}{7}}}{\sf{\times{\dfrac{4^{2}}{2}}}}$

$\sf{ = }{\sf{\dfrac{22}{7}}}{\sf{\times{\dfrac{16}{2}}}}$

$\sf{ = }{\sf{\dfrac{22}{7}}}{\sf{\times{8}}}$

$\sf{ = }{\sf{\dfrac{176}{7}}}$

$\bold{ = 25.142\: in.^{2}}$

Now :-

Area of parallelogram

$\bold{\red{ = Base }}{\bold{\red{\times{ Height }}}}$

Subsitute the required values,

$\sf{ = 10 }{\sf{\times{ 6 }}}$

$\bold{ = 60 \:in.^{2}}$

Thus, The area of parallelogram is 60 in.

Therefore,

Area of the given figure

= Area of semicircle + Area of parallelogram

Subsitute the required values,

$\sf{ = 25.142 + 60 }$

$\sf{ = 85.142\: in^{2}. }$

When round off to nearest Hundred

$\bold{ = 85.1 in.^{2}}$

Hence, The area of the given figure is 85.1 inches² .