High School

Identify the area of the polygon with vertices C(3,3), A(8,-2), S(3,-4), and H(0,-2).

A. 31.5 units²
B. 28 units²
C. 25 units²
D. 35.5 units²

Answer :

The vertices of the polygon form a trapezoid, and the area of the polygon is 28 unit squares.

The vertices are given as:

C = (3,3)

A = (8,-2)

S = (3,-4)

H = (0, -2)

The area of the polygon is calculated using:

[tex]A = \frac 12 \sum\limits^(n-1)_(k = 0)(x_ky_(k+1) - y_kx_(k+1))[/tex]

So, we have:

A = 1/2 * |(3 * -2 - 8 * 3 + 8 * -4 - 3 * -2 + 3 * -2 - 0 * -4 + 0 * 3 -3 * -2)|

Evaluate

A = 1/2 * |-56|

Remove the absolute bracket

A = 1/2 * 56

Evaluate the product

A= 28

Hence, the area of the polygon is 28 unit square

The vertices of the polygon form a trapezoid, and the area of the polygon is 28 unit squares

How to determine the area of the polygon?

The vertices are given as:

C = (3,3)

A = (8,-2)

S = (3,-4)

H = (0, -2)

The area of the polygon is calculated using:

[tex]A = \frac 12 \sum\limits^{n-1}_{k = 0}(x_ky_{k+1} - y_kx_{k+1})[/tex]

So, we have:

A = 1/2 * |(3 * -2 - 8 * 3 + 8 * -4 - 3 * -2 + 3 * -2 - 0 * -4 + 0 * 3 -3 * -2)|

Evaluate

A = 1/2 * |-56|

Remove the absolute bracket

A = 1/2 * 56

Evaluate the product

A= 28

Hence, the area of the polygon is 28 unit square

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