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S_A_V [24]
3 years ago
5

What is the area of trapezoid ABCD ?

Mathematics
1 answer:
8_murik_8 [283]3 years ago
8 0

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)

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