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

Answer:

16 square inches

Step-by-step 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:

$Total = A_1 + 4 * A_2$

$Total = 4 + 4 * 3$

$Total = 4 +12$

$Total = 16$