Hey. Let me help you on this one.
In order for us to solve this question, we need to break this problem apart. It will make it easier to understand.
In this problem, we see five different figures - four triangles, and one square.
If we want to get the complete net-surface area, we will need to find area of each figure individually, and then, add all values together.
Let's start with a square in the center. Formula for area of a square is [tex]S=a*a[/tex]. In this formula, [tex]S[/tex] stands for total area of a square, and stands for the length of one side.
Let's substitute the values!
[tex]S=4*4[/tex]
[tex]S=14[/tex]
Area of the square is 14 inches squared. Awesome! Now, let's find the area of all triangles.
We can see that one of the triangles has both measures - base, and the height. We need these two values in order for us to find the measure of the triangles.
Formula for the area of a triangle is [tex]S= \frac{a*b}{2} [/tex]. So, we need to multiply base length by the height length, and divide by two.
[tex]S= \frac{4*8}{2}[/tex]
[tex]S= \frac{32}{2} [/tex]
[tex]S=16[/tex]
Now, we know the area of one triangle. We have three other identical triangles, and in order for us to save time, let's just multiply this number by four.
[tex]16*4=64[/tex]
Triangles are 64 inches squared in total.
64 inches squared + 14 inches squared (square area) equals to 78 inches squared.
Answer: [tex]78^{2} [/tex] is the area of the figure
