91Ó°ÊÓ

Give a paragraph form of proof. Provide drawings as needed. Given: \(\quad\) Equilateral \(\triangle A B C\) with each side of length \(s\) Prove: \(\quad A_{A B C}=\frac{s^{2}}{4} \sqrt{3}\) (HINT: Use Heron's Formula.)

Use the formula \(A=\frac{1}{2} a P\) to find the area of the regular polygon described. In a regular octagon, the approximate ratio of the length of an apothem to the length of a side is \(6: 5 .\) For a regular octagon with an apothem of length \(15 \mathrm{cm},\) find the approximate area.

Assuming that the exact area of a sector determined by a \(40^{\circ}\) arc is \(\frac{9}{4} \pi \mathrm{cm}^{2},\) find the length of the radius of the circle.

Use the formula \(A=\frac{1}{2} a P\) to find the area of the regular polygon described. In a regular dodecagon (12 sides), the approximate ratio of the length of an apothem to the length of a side is 15: 8 For a regular dodecagon with a side of length \(12 \mathrm{ft}\), find the approximate area.

Use the formula \(A=\frac{1}{2} a P\) to find the area of the regular polygon described. In a regular dodecagon (12 sides), the approximate ratio of the length of an apothem to the length of a side is 15: 8 . For a regular dodecagon with an apothem of length \(12 \mathrm{ft}\), find the approximate area.

Use your calculator value of \(\pi\) to solve each problem. Round answers to the nearest integer. Find the length of the radius of a circle whose area is \(154 \mathrm{cm}^{2}\)

Use the formula \(A=\frac{1}{2} a P\) to find the area of the regular polygon described. In a regular octagon, the approximate ratio of the length of an apothem to the length of a side is \(6: 5 .\) For a regular octagon with a side of length \(15 \mathrm{ft}\), find the approximate area.

Use your calculator value of \(\pi\) to solve each problem. Round answers to the nearest integer. Find the length of the diameter of a circle whose circumference is 157 in.

A circle can be inscribed in an equilateral triangle, each of whose sides has length \(10 \mathrm{cm} .\) Find the area of that circle.

Use the formula \(A=\frac{1}{2} a P\) to find the area of the regular polygon described. In a regular polygon of 12 sides, the measure of each side is 2 in., and the measure of an apothem is exactly \((2+\sqrt{3})\) in. Find the exact area of this regular polygon.