Question

find the surface area of the figure below. as you can see the question has already been answered my teacher wants me to show how she got the answer this is due in an hour.

Answer 1

To find the surface area , first calculate the height of the triangle.

We can divide it into 2 right triangle and apply the pythagorean theorem:

c^2 = a^2+b^2

Where:

c= hypotenuse = 14

a = 14/2 = 7

b= height

Replacing:

14^2 = 7^2 + b^2

Solve for b

196= 49+b^2

196-49=b^2

147 = b^2

√147= b

b= 12.1 ft

Now, calculate the area of each rectangular face and each triangular face:

Area of a triangle = 1/2 x base x height = 1/2 x 14 x 12.1 = 84.8 ft2

Area of a rectangle = length x width = 14 x 10 = 140 ft2

Since it has 2 triangular faces and 3 rectangular faces

SA = 2 (84.7) + 3 (140) = 169.4+420= 589.7 ft2