Find the area in square feet of trapezoid ABCD with AB ≅ DC.

Question

Find the area in square feet of trapezoid ABCD with AB ≅ DC.

6 ft

4 ft

12 ft

Trapezoid A B C D contains four labeled vertices and a dashed line segment.

1. The left side starts at vertex A, goes down and to the left and ends at vertex B.
2. The bottom side is horizontal, starts at vertex B on the left and ends at vertex C on the right. It is labeled 12 ft.
3. The right side starts at vertex C, goes up and to the left and ends at vertex D.
4. The top side is horizontal, starts at vertex D on the right and ends at vertex A on the left. It is labeled 6 ft.
5. A dashed line segment goes down vertically from vertex A and meets side B C at a right angle. It is labeled 4 ft.

Answer 1

Hi Alyssa Z.

Question according to your information

AD = 6 ft

BC = 12 ft

Height, the dashed line = 4ft

Is that correct?

If that is so for your Trapezoid all you need to do is to plug the data in the formula for the area of a Trapezoid

h*(b₁ + b₂)/2

You can look this up in your text or on the internet, where the parameters are explained and you can identify them

I got 36

Give it a try.

Answer 2

If you draw a perpendicular line from D down to a point E on BC, then the two right triangles formed must be congruent (2 pairs of sides are congruent and they both have a right angle so congruent because of HL),

As the height of the trapezoid is 4 and AD is 6 area of rectangle = 4 x 6 = 24

The base of each right triangle must be (12-6)/2 = 3

So the area of the two triangles = 2 x 0.5 x 3 x 4 = 12

So area of trapezoid = 24 + 12 = 36