Question

What is the area of the polygon ?

Answer 1

Answer:

C)  99 in²

Step-by-step explanation:

you can divide this shape by drawing a horizontal line to create a 4x12" rectangle and a trapezoid with a height of (10-4) in and bases of 12 and 5"

area of rectangle:  12 x 4 = 48

area of trapezoid:  1/2(6)(12+5) = 3(17) = 51

total area = 48 + 51

total area = 99 in²

Answer 2

Answer:

C. 99

Step-by-step explanation:

First, we can split it into two rectangles and a right triangle: (see the image below)

The first rectangle has sides of 5, 10, 5, and 10.

The second has sides of 4, 7, 4, and 7.

The third has sides of 7, 6, and √85.

The first rectangle:

Because opposite sides are congruent in a rectangle, we know that the side across of the measure of 5 is also 5. The side across from 10 is also 10.

The second rectangle:

From the side with a measure of 4, draw a line across to meet the side of the first rectangle.

Because opposite sides are congruent, we know the other side is 4.

Because the whole entire bottom is 12, and the bottom of the first rectangle is 5, the side of the second rectangle must be 7.

This makes the other sides also 7.

The right triangle:

Because the lines are all perpendicular (indicated by right angle symbol), this is a right triangle.

We know that one of the sides is 7 (because of opposite sides being congruent in a rectangle). The whole side is the side of the first rectangle, so it's 10. That means that the other side of the right triangle is 6.

With the Pythagorean Theorem, we can find that the hypotenuse is √85.

Area of First Rectangle: A = l h

                                        A = (5) (10)

                                        A = 50

Area of Second Rectangle: A = l h

                                              A = (4) (7)

                                              A = 28

Area of Right Triangle: A = (1/2) (b) (h)

                                      A = (1/2) (7) (6)

                                      A = 21

21 + 28 + 50 = Area

Area = 99