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djyliett [7]
4 years ago
13

Helpppp!!!!!!!!!!!!!​

Mathematics
1 answer:
Eva8 [605]4 years ago
6 0

Answer:

A=37.5\ units^2

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

A=\frac{1}{2}[b1+b2]h

where

b1 and b2 are the parallel bases

h is the height of trapezoid (perpendicular distance between the two parallel bases)

In this problem the area is equal to

A=\frac{1}{2}[BC+AD]AB

we have the coordinates

A(-3,2),B(1,5),C(7,-3),D(0,-2)

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

step 1

Find the distance AB

A(-3,2),B(1,5

substitute in the formula

d=\sqrt{(5-2)^{2}+(1+3)^{2}}

d=\sqrt{(3)^{2}+(4)^{2}}

d_A_B=5\ units

step 2

Find the distance BC

B(1,5),C(7,-3)

substitute in the formula

d=\sqrt{(-3-5)^{2}+(7-1)^{2}}

d=\sqrt{(-8)^{2}+(6)^{2}}

d_B_C=10\ units

step 3

Find the distance AD

A(-3,2),D(0,-2)

substitute in the formula

d=\sqrt{(-2-2)^{2}+(0+3)^{2}}

d=\sqrt{(-4)^{2}+(3)^{2}}

d_A_D=5\ units

step 4

Find the area

A=\frac{1}{2}[BC+AD]AB

substitute the values

A=\frac{1}{2}[10+5]5

A=37.5\ units^2

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