Answer:
A) 288 units³
B) 144√2 ≈ 203.65 units²
C) 144(1+√2) ≈ 347.65 units²
Step-by-step explanation:
<h3>A)</h3>
The volume of a pyramid is given by the formula ...
V = 1/3Bh
where B is the area of the base, and h is the height. The base is a square with side length 12, so its area is
A = s² = 12² = 144
Then the volume is ...
V = 1/3(144)(6) = 288 . . . . cubic units
__
<h3>B)</h3>
To find the area of one of the triangular faces of the pyramid, we must first find the slant height. The slant height is the hypotenuse of a right triangle with legs equal to the pyramid height and half the base side length. Those are both 6 units, so the slant height is the hypotenuse of an isosceles right triangle with legs that are 6:
h = √(6² +6²) = 6√2
The area of the four faces is 4 times the area of one triangular face. So, the lateral area is ...
LA = 4(1/2)(12)(6√2) = 144√2 ≈ 203.65 . . . . square units
__
<h3>C)</h3>
The total surface area of the pyramid is the sum of the lateral area and the base area:
SA = 144√2 +144 = 144(1+√2) ≈ 347.65 . . . . square units
