Question

Step by step Help ?

Answer 1

Given:

The given figure consists of a triangle, a rectangle and a half circle.

The base of the triangle is 2 mi.

The height of the triangle is 4 mi.

The length of the rectangle is 9 mi.

The diameter of the half circle is 4 mi.

The radius of the half circle is 2 mi.

We need to determine the area of the enclosed figure.

Area of the triangle:

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

$A=\frac{1}{2}bh$

where b is the base and h is the height

Substituting b = 2 and h = 4, we get;

$A=\frac{1}{2}(2\times 4)$

$A=4 \ mi^2$

Thus, the area of the triangle is 4 mi²

Area of the rectangle:

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

$A=length \times width$

Substituting length = 9 mi and width = 4 mi, we get;

$A=9 \times 4$

$A=36 \ mi^2$

Thus, the area of the rectangle is 36 mi²

Area of the half circle:

The area of the half circle can be determined using the formula,

$A=\frac{\pi r^2}{2}$

Substituting r = 2, we get;

$A=\frac{(3.14)(2)^2}{2}$

$A=\frac{(3.14)(4)}{2}$

$A=\frac{12.56}{2}$

$A=6.28$

Thus, the area of the half circle is 6.28 mi²

Area of the enclosed figure:

The area of the entire figure can be determined by adding the area of the triangle, area of rectangle and area of the half circle.

Thus, we have;

Area = Area of triangle + Area of rectangle + Area of half circle

Substituting the values, we get;

$Area=4+36+6.28$

$Area = 46.28 \ mi^2$

Thus, the area of the enclosed figure is 46.28 mi²