To calculate the , we can use the known formula where P is the of the base, h is the height, and B is the of the base.
S=Ph+2B
Will calculate the perimeter of the base P, the area of the base B, and the surface area of the solid S one at a time.
Perimeter of the Base
The given is a with height 18 feet. The base is an with height 8 feet and base 14 feet.
The height of the triangle divides it into two . Also, the height the base of the triangle. Therefore, we have two right triangles with base length 14÷ 2= 7 feet and height 8 feet.
By finding the c, we will be able to find the perimeter of the base of the prism. Let's use the to find c.
c^2=a^2+b^2
c^2= 8^2+ 7^2
c=sqrt(113)
The length of the congruent sides of the base of the prism is sqrt(113) feet.
We now know the lengths of the three sides of the base. Let's add them to find the perimeter of the base.
P&= 14+ sqrt(113)+ sqrt(113)
P&= 14+2sqrt(113)
Area of the Base
Now, we can calculate the area of the base using the formula for the
B=1/2bh
B=1/2( 14)( 8)
B=56
The area of the base is 56 square feet.
Surface Area
We have enough information to find the surface area of the prism. Let's substitute P= 14+2sqrt(113), h= 18, and B=56 into the corresponding formula.
S=Ph+2B
S=( 14+2sqrt(113))( 18)+2( 56)
S=252+36sqrt(113)+2(56)
S=252+36sqrt(113)+112
S=364+36sqrt(113)
S=364+36(10.630145...)
S=364+382.685249...
S=746.685249...
S≈ 746.7
The surface area of the prism is about 746.7ft^2.
