a. 800[tex]m^{2}[/tex]
b. 96,568.54 ft^2
The formula for solving for surface area of a pyramid is: B + (1/2*P*l), with B being the area of the base, P being the perimeter of the base, and l being the slant of the pyramid.
Steps for a:
- 16*16 = 256 (this is the B)
- 16*4 = 64 (this is the P)
- (1/2*64*17) = 544 (17 is the slant)
- 256 + 544 = 800
Steps for b:
- 200*200 = 40,000 (this is the B)
- 200*4 = 800 (this is the P)
- This step is a bit tricky, but to find the slant of the pyramid, use the Pythagorean theorem [tex]a^{2} + b^{2} = c^{2}[/tex]: [tex]100^2 + 100^2 = 20,000[/tex]. Then, use the square root of 20,000 to find the slant (141.4213562
- (1/2*800*141.4213562) = 56,568.54248
- 40,000 + 56,568.54248 = 96,568.54 ft^2
Hope this helps!
