# A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for ππ .. 4 in L, Base 6in

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## Question:

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for ππ .. 4 in L, Base 6in

The area of the given figure is 38.13 in² and its perimeter is 23.42 in.

First, we will determine the area of the semicircle,

Area of a semicircle = Half area of a circle

Area of a circle =

∴ Area of semicircle =

From the diagram, the base of the figure (length of the rectangle) equals the diameter of the semicircle

∴ diameter = 6 in.

But

r = 3 in.

Now, from

Area of semicircle =

Area of the semicircle =

Area of the semicircle =

Area of the semicircle = 14.13 in².

For the rectangle,

Area of rectangle =

Length = 6 in.

and the width = 4 in.

∴ Area of the rectangle = 6 × 4

Area of the rectangle = 24 in².

Now, for the area of the figure,

Area of the figure = Area of the semicircle + Area of the rectangle

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∴ Area of the figure = 14.13 in². + 24 in².

Area of the figure = 38.13 in².

For the perimeter of the figure,

Perimeter is sum of all sides

Perimeter of the figure = Width of rectangle + Length of rectangle + Width of rectangle + length of the half circumference

First, we will determine the length of the half circumference,

Length of the half circumference =

Length of the half circumference = 3.14 × 3

Length of the half circumference = 9.42 in.

From

Perimeter of the figure = Width of rectangle + Length of rectangle + Width of rectangle + length of the half circumference

∴ Perimeter of the figure = 4 in. + 6 in. + 4 in. + 9.42 in.

Perimeter of the figure = 23.42 in.

Hence, the area of the figure is 38.13 in² and its perimeter is 23.42 in.

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