Answer:
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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