Given:
A square base pyramid whose base length is 10 in. and height of triangular surface is 4 in.
To find:
The surface area of the pyramid to the nearest whole number.
Solution:
A square base pyramid contains square base with edge 10 in. and 4 congruent triangles with base 10 in. and height 4 in.
Area of a square is
[tex]A_1=(edge)^2[/tex]
[tex]A_1=(10)^2[/tex]
[tex]A_1=100[/tex]
So, area of square base is 100 sq. in.
Area of a triangle is
[tex]A_2=\dfrac{1}{2}\times base\times height[/tex]
[tex]A_2=\dfrac{1}{2}\times 10\times 4[/tex]
[tex]A_2=20[/tex]
So, area of each triangular surface is 20 sq. in.
Now, the total surface area of the pyramid is
Total area = Area of square base + Area of 4 congruent triangles.
[tex]A=A_1+4\times A_2[/tex]
[tex]A=100+4\times 20[/tex]
[tex]A=100+80[/tex]
[tex]A=180[/tex]
Therefore, the area of the pyramid is 180 sq. in.
