A regular heptagon has an apothem of approximately 7.3 yd and a perimeter of approximately 49.0 yds. Based on these measurements, what is the area of the heptagon?

Question

AZ · Answer

We have a heptagon (which means it's a polygon with 7 sides)

The apothem is the distance from the center to the midpoint of a side.
This is an example shown on a hexagon (six sided figure)

AZ · Answer

To calculate the area of a regular heptagon, we can just add up the area of the 7 triangles

Area of triangle = 1/2 * base * height

We can calculate the base from the perimeter.
The perimeter of the heptagon is the sum of all the sides.

To find the length of each side, just divide the perimeter by 7

49 /7 = ??

That's the base of the triangle

The apothem is the height of the triangle which is 7.3 yards

AZ · Answer

So to find the area of the heptagon, find the area of one triangle

area = 1/2 * base * height

plug in the numbers you got from my previous reply
the height is 7.3
the base is going to be 49/7 which is??

and so that's the area of one triangle

The heptagon has 7 triangles so multiply that area by 7. That will be your final answer.

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