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1 year ago

What is the area of the following polygon?

Mathematics

1 answer:

muminat1 year ago

6 0

The area of the polygon is 25.5 square units

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

From the figure, we have the following coordinates

A = (-2, 1)

B = (3, 2)

C = (5, -3)

D = (-1, -3)

The area of the polygon is then calculated as:

A = 0.5 * |(x1y2 - x2y1) + (x2y3 - x3y2) + (x3y4 - x4y3) + (x4y1 - x1y4)|

Substitute the known values in the above equation

Area = 0.5 * |(-2 * 2 - 3 * 1) + (3 * -3 - 5 * 2) + (5 * -3 + 1 * -3) + (-1 * 1 + 2 * -3)|

Evaluate the sum of products

Area = 0.5 * |-51|

Remove the absolute bracket

Area = 0.5 * 51

Evaluate the product

Area = 25.5

Hence, the area of the polygon is 25.5 square units

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Answer:

Option A.

Step-by-step explanation:

Distance between Bob and the center of the mountain at the base = 19,427.5 ft.

Angle of elevation to the top of the mountain = 25°11'

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1 degree = 60 minutes

1/60 degree = 1 minute

$25^{\circ}11'=25^{\circ}+\frac{11}{60}{\circ}\Rightarrow 25^{\circ}+0.183^{\circ}=25.183^{\circ}$

Let the height of the mountain be h.

In a right angled triangle

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$\tan(25.183^{\circ}) = \frac{h}{19427.5}$

$\tan(25.183^{\circ})\times 19427.5 = h$

$h=0.4702\times 19427.5$

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