Mathematics: Find the area of the polygon pls

Find the area of the polygon pls - id10996318, zach8782

claudialopez093

09.04.2022

Given:

The figure of a polygon.

To find:

The area of the polygon.

Solution:

Area of a triangle is

$Area=\dfrac{1}{2}\times Base\times Height$

Area of trapezoid is

$Area=\dfrac{1}{2}(a+b)h$

Where, a, b are bases and h is the height.

The area of the triangle with base 6 cm and height 8 cm is

$A_1=\dfrac{1}{2}\times 6\times 8$

A_1=24

Height of the trapezoid is $13-8=5\ \text{cm}$ and the bases are 6 cm, 12 cm. So, the area of the trapezoid is

$A_2=\dfrac{1}{2}(6+12)(5)$

$A_2=\dfrac{1}{2}(18)(5)$

A_2=(9)(5)

A_2=45

Now, the total area of the polygon is

A=A_1+A_2

A=24+45

A=69

Therefore, the area of the polygon is 69 sq. cm.

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