Find the area of quadrilateral ABCD. Round the area to the nearest whole number, if necessary.

Mathematics

1 answer:

andrew11 [14]2 years ago

8 0

The area of the quadrilateral ABCD is 26 square units

<h3>How to find the area of quadrilateral ABCD?</h3>

The quadrilateral ABCD is a trapezoid, and it has the following parameters:

Parallel bases = BC and AD

Height = CE

The lengths of these sides can be calculated using

d = √[(x2 - x1)^2 +(y2 - y1)^2]

So, we have

BC = √[(0 - 4)^2 +(3 + 1)^2] = 4√2

AD = √[(-5 - 4)^2 +(4 + 5)^2] = 9√2

CE = √[(2 - 4)^2 +(-3 + 1)^2] = 2√2

The area of the quadrilateral ABCD is then calculated as

Area = 0.5 * (BC + AD) * CE

This gives

Area = 0.5 * (4√2 + 9√2) * 2√2

Evaluate

Area = 26

Hence, the area of the quadrilateral ABCD is 26 square units

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