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GenaCL600 [577]
3 years ago
10

What is the area of the rectangle? shoe your work! do not round anything until the very end and round your final answer to the t

enths place.

Mathematics
1 answer:
weeeeeb [17]3 years ago
4 0

Answer:

The area of the rectangle is 42 units^2

Step-by-step explanation:

we know that

The area of rectangle is equal to

A=LW

In this problem

AB=DC

BC=AD

see the attached figure with letters to better understand the problem

we have that

L=BC\\W=AB

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

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

we have the points

A(2,-1),B(5,2),C(12,-5),D(9,-8)

<em>Find out the distance BC</em>

we have

B(5,2),C(12,-5)

substitute in the formula

d=\sqrt{(-5-2)^{2}+(12-5)^{2}}

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

d_B_C=\sqrt{98}\ units

<em>Find out the distance AB</em>

we have

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

substitute in the formula

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

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

d_A_B=\sqrt{18}\ units

<em>Find out the area</em>

A=(L)(W)

we have

L=d_B_C=\sqrt{98}\ units

W=d_A_B=\sqrt{18}\ units

substitute

A=(\sqrt{98})(\sqrt{18})=42.0\ units^2

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