Question

What is the area of the composite figure?

(6pie + 4) cm^2
(6pie + 16) cm^2
(12pie + 4) cm^2
(12pie + 16) cm^2​

Answer 1

Given:

The composite figure consists of a square and three semicircles.

Given that the half of the side of the square is 2 cm.

From the figure, the other half of the same side is also equal, then the side of the square is 2 + 2 = 4 cm.

We need to determine the area of the composite figure.

Area of the square:

The area of the square can be determined using the formula,

`A=s^2`

where s is the side length of the square.

Substituting s =4 ,we get;

`A=4^2`

`A=16`

Thus, the area of the square is 16 cm²

Area of the semicircle:

The area of the semicircle can be determined using the formula,

`A=(\pi r^2)/(2)`

The radius of the semicircle is 2 cm.

Substituting r = 2 in the above formula, we get;

`A=(\pi 4)/(2)`

`A=2 \pi`

Thus, the area of the semicircle is 2π

Area of the composite figure:

The area of the composite figure can be determined by adding the area of the square and the three semicircles.

Thus, we have;

Area = Area of square + (3 × Area of semicircle)

Substituting the values, we have;

`Area = 16 +(3 * 2 \pi)`

`Area = 16+6 \pi`

Thus, the area of the composite figure is
`(6 \pi +16) \ cm^2`

Hence, Option b is the correct answer.