Question

Question 4 (Essay Worth 10 points)

Answer 1

Answer:

12 sq. units

Step-by-step explanation:

Because this is an irregular polygon, we can break the figure into simpler shapes and add the areas together.  

For the left triangle, use the formula $\frac{1}{2}$ (b × h)

$\frac{1}{2}$ (2 × 2)

$\frac{1}{2}$ (4) = 2 sq. units

For the top triangle:

$\frac{1}{2}$ (4 × 2)

$\frac{1}{2}$ (8) = 4 sq. units

For the middle rectangle, use the formula b × h

(3 × 2) = 6 sq. units

Now add together all the areas.

2 qu. units + 4 sq. units + 6 sq. units = 12 sq. units

Hope this helps~!

Answer 2

Answer:

We can split the shape into two figures;

Triangle

Trapezoid

The above shape will be a triangle and the shape below it will be considered the trapezoid.

First let's know the formula of their areas for the two:

Formula for area of a trapezoid is

A = 1/2(b1 + b2) x h

Formula for area of triangle is

A = BH x 1/2

Now let's figure out the base and height of the triangle:

4 is the base and 2 is the height, now plug in our values into the formula:

A = BH x 1/2

A = 4 x 2 x 1/2

A = 8 x 1/2

A = 8/2

A = 4, the area of the triangle is 4

Now the trapezoid's bases and height:

The bottom base is 5, and the top base is 3, our height is 2

So plug in those values into the formula;

A = 1/2(b1 + b2) x h

A = 1/2(5 + 3) x 2

A = 5/2 + 3/2 x 2

A = 8/2 x 2

A = 16/2 which simplifies to 8

Now add the areas for those two shapes:

4(triangle) + 8(trapezoid) = 12 is your answer.