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QuestionCalculate the area of a regular 7-sided polygon with an apothem of 8 m and side length of 7.7 m. Round to the nearest tenth. [?] m2\mathrm{m}^{2}

Studdy Solution

STEP 1

Assumptions1. The polygon is regular (all sides and angles are equal) . The number of sides of the polygon is73. The apothem (the line segment from the center of the polygon perpendicular to a side) is8 meters4. The length of each side of the polygon is7.7 meters

STEP 2

The area of a regular polygon can be found using the formulaArea=12×Perimeter×ApothemArea = \frac{1}{2} \times Perimeter \times Apothem

STEP 3

First, we need to find the perimeter of the polygon. The perimeter of a regular polygon is the length of one side times the number of sides.
Perimeter=Number of sides×Length of one sidePerimeter = Number\, of\, sides \times Length\, of\, one\, side

STEP 4

Plug in the given values for the number of sides and the length of one side to calculate the perimeter.
Perimeter=7×7.7 metersPerimeter =7 \times7.7\, meters

STEP 5

Calculate the perimeter.
Perimeter=7×7.7 meters=53.9 metersPerimeter =7 \times7.7\, meters =53.9\, meters

STEP 6

Now that we have the perimeter, we can find the area of the polygon using the formula from2.
Area=12×Perimeter×ApothemArea = \frac{1}{2} \times Perimeter \times Apothem

STEP 7

Plug in the values for the perimeter and the apothem to calculate the area.
Area=12×53.9 meters× metersArea = \frac{1}{2} \times53.9\, meters \times\, meters

STEP 8

Calculate the area.
Area=12×53. meters×8 meters=215.6 m2Area = \frac{1}{2} \times53.\, meters \times8\, meters =215.6\, m^{2}The area of the regular polygon is approximately215.6 square meters.

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