Question

A model of a soccer ball is made up of regular pentagons and hexagons.

Answer 1

An apothem is a line from the center of a regular polygon at right angles to any of its sides.

For part A,

We want to find area of pentagon (5 sided figure) given apothem is 1.38 in and side length as 2 inch.

If we look at the picture shown (attached), we can see that a triangle is formed. What is the area of this triangle?

$A=0.5bh\\A=0.5(1)(1.38)\\A=0.69$ square inches

How many such triangles are there in a pentagon? 10. So we multiply 0.69 by 10 to get total area of pentagon.

Area of Pentagon = $0.69*10=6.9$ square inches.

For part B,

We want to find area of hexagon (6 sided figure) given apothem is 1.73 in and side length as 2 inch.

If we look at the picture shown (attached), we can see that a triangle is formed. What is the area of this triangle?

$A=0.5bh\\A=0.5(1)(1.73)\\A=0.865$ square inches

How many such triangles are there in a hexagon? 12. So we multiply 0.865 by 12 to get total area of hexagon.

Area of Hexagon = $0.865*12=10.4$ square inches.

ANSWER:

Area of Pentagon is 6.9 square inches.

Area of Hexagon is 10.4 square inches.