Question

Find the area of ABCD with vertices A(-5,2), B(-3,2), C(-2,-5),
D(-4,-5).

Answer 1

• 14 units²

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Given

• Vertices A(-5,2), B(-3,2), C(-2,-5), D(-4,-5)

To find

• The area of ABCD

Solution

We can observe that:

1. AB and CD are horizontal segments, since both endpoints have same y-coordinates:

• A and B have y = 2, C and D have y = - 5

2. AB and CD are of same length:

• AB = - 3 - (-5) = 2,
• CD = - 2 - (-4) = 2.

It means the ABCD is a parallelogram, since two opposite sides are parallel and of same length.

The area of parallelogram is:

• A = bh, where b- base length, h - height

We know the length of the base, it is found above, 2 units.

The height is the difference of y- coordinates:

• h = 2 - (-5) = 7

The area is:

• A = 2*7 = 14 units²