Answer:
[tex]A_{L} =125 in^{2}[/tex]
Step-by-step explanation:
Let's break down the pyramid in different bidimensional figures. As you can see in the image, the pyramid has 5 total sides: 4 of them are triangles and 1 is a square (the bottom). Therefore, the total area of this pyramid is given by the area of 4 triangles of base 5 in and height 10 in, and a square whose sides measure 5 in.
1. Write an expression and find the area of all triangles.
We already know the formula for the area of a triangle: [tex]A=\frac{b*h}{2}[/tex], where b is the measure of the base of the triangle, and h is the height is the triangle. We have 4 triangles, therefore, let's multiply this formula by 4 and calculate.
[tex]A=4*(\frac{b*h}{2})=\\ \\ \\A=4*(\frac{(5)(10)}{2})=\\ \\A=4*(\frac{50}{2})=\\ \\A=4*(25)=\\ \\A=100[/tex]
2. Find the area of the bottom side.
The bottom side is a square whose whose sides measure 5 in. Hence, it's area is:
[tex]A=a^{2}[/tex], where a is the length of one side. Then:
[tex]A=(5)^{2}\\ \\A=25[/tex]
3. Add up all the areas to get the total alteral area of this pyramid.
[tex]A_{L} =100+25=125 in^{2}[/tex]
