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uranmaximum [27]
2 years ago
9

The locations:

Mathematics
1 answer:
GREYUIT [131]2 years ago
7 0

The quadrilateral is a trapezoid and the area of the quadrilateral is 85.04 square units

<h3>How to determine the quadrilateral?</h3>

The vertices are given as:

A:(-2, 3) B:(4, -6) C:(10, 2) D:(6, 8)

Next, we plot the vertices (see attachment)

From the attached graph, we can see that the quadrilateral is a trapezoid

<h3>How to determine the area?</h3>

From the plot, we have the following features:

Height: AD

Parallel sides: CD and AB

Calculate the lengths using:

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

So, we have:

AD = \sqrt{(-2 -6)^2 + (3 -8)^2}

AD = \sqrt{89}

CD = \sqrt{(10 -6)^2 + (2 -8)^2}

CD = \sqrt{52}

AB = \sqrt{(-2 -4)^2 + (3 +6)^2}

AB = \sqrt{117}

The area is then calculated as:

Area = 0.5 * (CD + AB) * AD

This gives

Area = 0.5 * (√52 + √117) * √89

Evaluate

Area = 85.04

Hence, the area of the quadrilateral is 85.04 square units

Read more about areas at:

brainly.com/question/24487155

#SPJ1

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