Question

Please help with these two questions!!!!!

Answer 1

These are two questions and two answers.

Question 1. Area of an hexagon with a radius of 8 and an apothem of 4√3.

Answer: 96√3 unit²

Explanation:

1) Divide the hexagon in 6 equilateral triangles.

2) The side of each equilateral triangle is equal to the given radius: 8 units.

3) The height of each equilateral triangle is equal to the apothema: 4√3 unit.

4) The area of each equilateral triangle is:

base × heiight / 2 = 8 unit × 4√3 unit/ 2 = 16√3 unit²

5) The area of the hexagon is 6 times the area of one equilateral triangle:

6×16√3 unit²= 96√3 uni²

Question 2. Area of a madallion.


Answer:863.94 in²

Explanation:

1) The shape of the blue part is a ring with the outer radius of the circumference of 113.097 in and the inner radius equal to 7 in.

2) Outer radius

circumference = 2π r = 113.097 ⇒ r = 113.097 in / (2π) = 18 in

3) Area of the outer circle = π r² = π (18 in)² = 1017.88 in²

4) Area of the inner circle, with r = 7in = π r² = π (7in)² = 153.94 in²

5) Area of the ring (blue part) = 1017.88 in² - 153.94 in² = 863.94 in²