Answer:
16 square inches
Step-by-step explanation:
Given
Triangle (4)
[tex]Height = 3[/tex]
[tex]Base = 2[/tex]
Square (1)
[tex]Length = 2[/tex]
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:
[tex]Area =Length^2[/tex]
[tex]A_1= 2^2[/tex]
[tex]A_1= 4[/tex]
[tex]The\ area\ of\ 1[/tex] of the triangles is:
[tex]Area = 0.5 * Base * Height[/tex]
[tex]A_2 = 0.5* 3 * 2[/tex]
[tex]A_2 = 3[/tex]
For the 4 triangle, the area is 4 * A2
So, the total area is:
[tex]Total = A_1 + 4 * A_2[/tex]
[tex]Total = 4 + 4 * 3[/tex]
[tex]Total = 4 +12[/tex]
[tex]Total = 16[/tex]
