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Find the perimeter and the area of the polygon with the given vertices.

The coordinates of the four points are S(-11,-8), T(-11,0), U(0,0), and V(0,-8).

The perimeter is
units.

The area is
square units.

2 Answers

1 vote

Answer:

mark me brilliant

Explanation:

We can find the perimeter of the polygon by adding up the lengths of its sides, which can be found using the distance formula:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

where d is the distance between the two points with coordinates (x1, y1) and (x2, y2).

The sides of the polygon are:

- SV, with endpoints (-11,-8) and (0,-8)

- UT, with endpoints (0,0) and (-11,0)

- TS, with endpoints (-11,0) and (-11,-8)

- UV, with endpoints (0,0) and (0,-8)

Using the distance formula for each side, we get:

- SV = √[(-11 - 0)^2 + (-8 - (-8))^2] = 11 units

- UT = √[(0 - (-11))^2 + (0 - 0)^2] = 11 units

- TS = √[(-11 - (-11))^2 + (0 - (-8))^2] = 8 units

- UV = √[(0 - 0)^2 + (-8 - 0)^2] = 8 units

Therefore, the perimeter of the polygon is:

Perimeter = SV + UT + TS + UV = 11 + 11 + 8 + 8 = 38 units

To find the area of the polygon, we can divide it into two triangles: STU and SVU. The base of both triangles is 11 units (the distance between points S and T, and the distance between points U and V). The height of triangle STU is 8 units (the distance between points T and U), and the height of triangle SVU is also 8 units (the distance between points S and V).

The area of each triangle can be found using the formula:

Area = (1/2) x base x height

For triangle STU:

Area(STU) = (1/2) x 11 units x 8 units = 44 square units

For triangle SVU:

Area(SVU) = (1/2) x 11 units x 8 units = 44 square units

Therefore, the total area of the polygon is:

Area = Area(STU) + Area(SVU) = 44 + 44 = 88 square units

User Avimoondra
by
7.4k points
4 votes

Answer:

Perimeter= approximately 43.2

Area=88

User Alcalde
by
8.2k points