Question

Please help! How much bigger is the area of Polygon A that id not covered by Polygon B and C than the area of Polygon B is not covered by Polygon C?

Answer 1

b. 32.70531 square inches

Explanation:

We know the length of the side of polygon A, so we calculate the length of the other sides, knowing their relation to the perimeter.

Polygon C = 1 inch

Polygon A = 4 * 1 inches = 4 inches

Polygon B = 1/2 * 4 inches = 2 inches

The area of the heptagon is calculated using the formula:

`A=(7\cdot a^2)/(4\cdot\:\tan\left((180°)/(7)\right))`

We obtain this area from the following:

By means of trigonometric ratios we obtain the formula.

We use the formula to calculate the Area of each polygon, like this:

`\begin{gathered} A_A=(7\cdot4^2)/(4\cdot\:\tan\left((180°)/(7)\right))=58.14259 \\ \\ \\ A_B=(7\cdot\:2^2)/(4\cdot\:\:\tan\left((180°)/(7)\right))=14.53564 \\ \\ \\ A_C=(7\cdot\:1^2)/(4\cdot\:\:\tan\left((180°)/(7)\right))=3.63391 \end{gathered}`

We calculate the differences between the areas of A and B and then the difference between the areas of B and C, and finally the difference between the areas obtained

`\begin{gathered} A_1=A_A-A_B=_58.14259-14.53564=43.60695 \\ \\ A_2=A_B-A_C=14.53564-3.63391=10.90173 \\ \\ A=A_1-A_2=43.60695-10.90173=32.70522\cong32.70531 \end{gathered}`

Therefore, the correct answer is b. 32.70531 square inches