Question

A semicircle and a quarter circle are attached to the sides of a rectangle as shown. What is the area of this figure? Use 3.14 for pi. Enter your answer in the box. Round only your final answer to the nearest whole number.

Answer 1

Explanation:

solve it a lil diff - area of the figure is the same as that of a 12x2 rectangle plus 12-dia circle minus a quarter of that 12-dia circle.

rectangle area=12x2=24cm^2

full 12-dia circle area=pi(dia/2)^2=3.14(12/2)^2=3.14x36

quarter area of the 12-dia circle=3.14x36/4=3.14x9

total area=24+3.14x36-3.14x9

=108.78=109cm^2

Answer 2

109 cm^2

Explanation:

We will find the area of the semi circle at the bottom.

The diameter is 12 so the radius is 6

A semicircle is 1/2 of a circle so it has 1/2 the area

A = pi r^2

A semicircle = 1/2 pi r^2

= 1/2 *pi *6^2

= 1/2 *3.14 *36

= 56.52

Next is the strip

It is rectangular with length 12 and width 2

A = l*w = 2*12 = 24

Finally we have the quarter circle

A quarter = 1/4 of the area of a circle

The radius is 6

A quarter = 1/4 pi r^2

=1/4 pi *6^2

= 1/4 *3.14 *36

= 28.26

Sum the areas together

A semi circle + A rectangle * A quarter circle

56.52 + 24+ 28.26

108.78 cm^2

Rounding to the nearest whole number

109 cm^2