Answer:
159.21 units²
Step-by-step explanation:
Half the side length can be found from ...
... s/2 = 7×tan(360°/20) ≈ 7×0.324920 ≈ 2.27444 . . . units
The area is then the product of half the perimeter and the given apothem:
... Area = 10(s/2)×7 ≈ 70×2.27444 ≈ 159.21 . . . . units²
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Check
The area of the inscribed circle will be πr² = π×49 ≈ 153.94 units². This must be slightly smaller than the area of the decagon, and it is.
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Comment on the area formula
In this situation, you are often taugth to us the formula
... A = 1/2Pa . . . . . where P = perimeter and a is the apothem.
Given only the apothem, we find we can compute the area from the equivalent formula ...
... A = n·a²·tan(180°/n) . . . . where n is the number of sides
