Question

I would love some help on this question it's quite unique compared to the others I've dealt with?

Answer 1

Given: The figure:

Required: Area of the figure.

Step-by-step explanation:

Observe the figure carefully.

It has one square with side 50+50 = 100 units.

It has four partial circles, with radius 50 units.

Area of the figure is

Area of 1 square + The area of four partial circles.

Now, area of square with side 100 units is

`\begin{gathered} A_1=(100)^2 \\ A_1=10000 \end{gathered}`

Now, the circles are not complete, they are partial. Since the angle is shown to be right angles, so 90/360, that is 1/4 th of the circle is not there. So we have to calculate area of 3/4 th circle only.

Now, area of 4 (3/4)th circles is

`\begin{gathered} A_2=4*(3)/(4)*\pi* r^2 \\ A_2=4*(3)/(4)*3.1416*50^2 \end{gathered}`

Calculating

`\begin{gathered} A_2=3*3.1416*2500 \\ A_2=23562 \end{gathered}`

So total area

`\begin{gathered} A=A_1+A_2 \\ A=10000+23562=33562\text{ square units} \end{gathered}`

Final Answer: Option D is correct.