Question

What is the area of trapezoid ABCD ?

Enter your answer as a decimal or whole number in the box. Do not round at any steps.

units²

Answer 1

Answer:

The area of the trapezoid ABCD = 37.5 sq. units.

Step-by-step explanation:

If we join points B and D on the figure given with the question.

Then area of the trapezoid ABCD = area of Δ ABD + area of Δ BDC

Now, area of Δ ABD = $\frac{1}{2} |- 3(5 - (- 2)) + 1(- 2 - 2) + 0(2 - 5)| = 12.5$ sq, units.

Again area of Δ BDC = $\frac{1}{2} |1(- 2 -(- 3)) +0(- 3 - 5)+ 7(5 - (- 2))|$ = 25 sq, units

Therefore, the area of the trapezoid ABCD = 12.5 + 25 = 37.5 sq. units.

We know the formula of area of a triangle having vertices $(x_{1}, y_{1})$, $(x_{2}, y_{2})$, and $(x_{3}, y_{3})$ will be equal to  

Δ = $\frac{1}{2} |x_{1} (y_{2} - y_{3})+ x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |$ (Answer)