Question

What is the total surface area of the rectangular pyramid below? A rectangular pyramid. The rectangular base has a length of 16 feet and width of 12 feet. 2 triangular sides have a base of 16 feet and height of 14 feet. 2 triangular sides have a base of 12 feet and height of 15 feet. 404 square feet 596 square feet 788 square feet 1,000 square feet

Answer 1

B. 596 Square Feet

Explanation:

Simple Answer..

Answer 2

The answer is 596 square feet

Explanation:

Recall the following formulas for area:

Rectangle of lenght l and width w:
`w\cdotl`

Triangle of base b and height h:
`(b\cdot h)/(2)`

In our case, since we have a pyramid with rectangular base, so we have 5 sides: the rectangular base and 4 triangles, that are grouped in two pairs of identicall triangles. Let us call the triangles T1 and T2. Then the total surface area is given by

surface area = Area of the base + 2*Area of T1 + 2* Area of T2

The base is a rectangle of lenght 16 and width 12, so the area is 16*12 = 192.

T1 is a triangle of base 16 and height 14, so it has area 16*14/2 = 112.

T2 is a triangle of base 12 and height 15, so it has area 15*12/2 = 90.

So the total area is

Area = 192+2*112+2*90 = 596.