Question

A 4 pointed star is created with for isosceles triangle and a square as shown below if the height of each triangle is 3 inches in one side of the square is 2 inches what is the area in square inches of the star

Answer 1

16 square inches

Explanation:

Given

Triangle (4)

`Height = 3`

`Base = 2`

Square (1)

`Length = 2`

Required

The surface area of the star

This is calculated as the area of the square added to the area of the 4 triangles.

The area of the square is:

`Area =Length^2`

`A_1= 2^2`

`A_1= 4`

`The\ area\ of\ 1` of the triangles is:

`Area = 0.5 * Base * Height`

`A_2 = 0.5* 3 * 2`

`A_2 = 3`

For the 4 triangle, the area is 4 * A2

So, the total area is:

`Total = A_1 + 4 * A_2`

`Total = 4 + 4 * 3`

`Total = 4 +12`

`Total = 16`