Question

What is the area of this polygon?

Enter your answer in the box.

units²

Answer 1

Area of polygon = 45 units²

Explanation:

Given : The figure attached of the polygon.

To find : What is the area of this polygon?

Solution :

To find the area we divide polygon into two areas by creating a line between F and S.

The two area form are triangle FNS and rectangle FWCS.

In triangle FNS,

Area of triangle is
`A=(1)/(2)* \text{Base}* \text{Height}`

The Base is unit from F to S is 9 unit (add each block).

The height is unit from N to base is 6 unit.

Area of triangle is
`A_t=(1)/(2)* 9* 6`

`A_t=27\ unit^2`

In rectangle FWCS,

Area of rectangle is
`A=\text{Length}* \text{Width}`

The Length is unit from F to S is 9 unit.

The Width is unit from F to W is 2 unit.

Area of rectangle is
`A_r=9* 2`

`A_r=18\ unit^2`

Area of polygon = Area of triangle + Area of rectangle

Area of polygon =27+ 18

Area of polygon = 45 units²

Answer 2

45 sq. units

Explanation:

We can draw a segment from F to S, splitting this figure into a rectangle and a triangle.

The area of a rectangle is given by the formula A=lw, where l is the length and w is the width.

The width of this figure is the distance of FW; this is 2. The length of this figure is the distance of WC; this is 9. This makes the area of the rectangle A=2(9) = 18 sq. units.

The area of a triangle is given by the formula A=1/2(b)(h), where b is the base and h is the height.

The base of the triangle is given by the distance of FS; this is 9. The height of the triangle is given from N to segment FS; this is 6. This makes the area of the triangle A=1/2(6)(9) = 27 sq. units.

This makes the total area 18+27 = 45 sq. units.