Question

This figure is made up of a rectangle and parallelogram. What is the area of this figure?


Enter your answer in the box. Do not round any side lengths.

What is the area of this polygon?

 

Enter your answer in the box.

Answer 1

Answer: 26 units

I don't have the answer to the second picture. That wasn't on my test

Explanation:

Answer 2

QUESTION 1

The given figure is made up of a parallelogram and a rectangle.

The area of the parallelogram is

`=base* height`

The base of the parallelogram is 6 units (Just count the boxes).

The height is also 1 unit.

This implies that the area of the parallelogram is

`=6* 1 \:units^2`

`=6\:units^2`

To find the area of the rectangle, we need to find the width and the length using the distance formula or the Pythagoras Theorem.

Using the Pythagoras Theorem,

`l^2=a^2+b^2`

`\Rightarrow l^2=2^2+6^2`

`\Rightarrow l^2=4+36`

`\Rightarrow l^2=40`

`\Rightarrow l=√(40)`

`\Rightarrow l=2√(10)`

Similarly,

`w^2=1^2+3^2`

`\Rightarrow w^2=1+9`

`\Rightarrow w^2=10`

`\Rightarrow w=√(10)`

The area of the rectangle is

`Area=l* w`

We substitute the values into the formula to obtain;

`Area=2√(10)* √(10)`

`Area=2*10`

`Area=20\:units^2`

The area of the figure is

`=20+6`

`=26\:units^2`

QUESTION 2

We can divide the given polygon into two parts to obtain a triangle and a rectangle. See diagram in attachment.

The area of the triangular portion is

`=(1)/(2)* base* height.`

`=(1)/(2)* 9* 6.`

`=9* 3.`

`=27\:units^2.`

The area of the rectangle is

`=l* w`

`=9* 2`

`=18\:units^2`

The area of the polygon is

`=27+18\:units^2`

`=45\:units^2`