Question

What is the area of the irregular pentagon

a. 43


b. 105



C)

108 in2



D)

114 in2

Answer 1

b.
`\text{105 in}^2`

Explanation:

We have been given an image of an irregular pentagon and we are asked to find the area of our given pentagon.

To find the area of our given pentagon, we will divide it into parts by dropping an altitude from the 9 inch side to the 12 inch side. This altitude will divide our given pentagon into one rectangle and one trapezoid.

The area of pentagon will be equal to area of rectangle plus area of trapezoid.

The sides of rectangle will be 9 inch and 8 inches.

`\text{Area of rectangular part}=\text{9 in}*\text{8 in}=\text{72 in}^2`

`\text{Area of trapezoid}=(h)/(2)* (a+b)`, where, a and b represents the length of parallel sides of trapezoid.

h = height of the trapezoid.

When we drop an altitude to the 12 inch side, it will give us the height of trapezoid as: 12-9=3 inch.

`\text{Area of trapezoid}=(3)/(2)* (8+14)`

`\text{Area of trapezoid}=(3)/(2)* (22)`

`\text{Area of trapezoid}=3* 11`

`\text{Area of trapezoid}=33`

`\text{Area of pentagon}=\text{Area of rectangle}+\text{Area of trapezoid}`

`\text{Area of pentagon}=\text{72 in}^2+\text{33 in}^2`

`\text{Area of pentagon}=\text{105 in}^2`

Therefore, the area of our given pentagon will be 105 square inches and option 'b' is the correct choice.

Answer 2

The area = 105 in² ⇒ answer (b)

Explanation:

Lets divide the figure into:

* rectangle of dimensions 8 in and 9 in

* trapezium with parallel bases 8 in and 14 in with height 3 in (12 - 9)

∵ Area rectangle = 8 × 9 = 72 in²

∵ Area trapezium = (8 + 14)/2 × 3 = 11 × 3 = 33 in²

∴ The area of the irregular pentagon = 72 + 33 = 105 in²