Question

This figure is made from a square and part of a circle. What is the area of the figure, to the nearest whole number square unit?

Answer 1

Answer: 242 sq. units

Step-by-step explanation:

It is given that it is made from a part of a circle, let us take the area of the circle with the radius 8.

Now, through the formula $\pi r^{2}$, we get that the area of the circle is 201.1 sq. units (Approx.)

But since the angle between them is 90°, we can say that the part is 1/4th of the actual circle, thereby having 1/4th area = 50.27 sq. units (Approx.)

The rest of the parts of the given figure can be divided into :-

i) A rectangle with the measures of 16, 8 giving the area of 128 sq. units.

ii) A square with the measure of each side 8, giving the area of 64 sq. units.

Now, adding all the three areas of the parts of the figure,

→ 50.27 + 64 + 128

⇒ 242.27 square units.

We get the total area of the figure to the 242 sq. units rounded of to the nearest whole number.