Question

What is the area of this polygon? Enter your answer in the box. units²

Answer 1

Answer:

45 sq. units

Step-by-step 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.

Answer 2

Answer:

Area of polygon = 45 units²

Step-by-step 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 $A=\frac{1}{2}\times \text{Base}\times \text{Height}$

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 $A_t=\frac{1}{2}\times 9\times 6$

$A_t=27\ unit^2$

In rectangle FWCS,

Area of rectangle is $A=\text{Length}\times \text{Width}$

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 $A_r=9\times 2$

$A_r=18\ unit^2$

Area of polygon = Area of triangle + Area of rectangle

Area of polygon =27+ 18

Area of polygon = 45 units²