Question

the base of the figure shown is a cube with sides that are 12 inches long. the total height of the figure is 20 inches. the slant height of the pyramid on top of the cube is 10 inches. what is the total surface area of the figure?

Answer 1

Answer: 960 square inches

Step-by-step explanation:

Here, the base of pyramid is a cube with side 12 inches, the total height is 20 cm and the slant height of the pyramid on top of the cube is 10 inches.

Since, With help of the below diagram,

We can say that,

The surface area or the total area of the given pyramid = 5 × Total area of cube having side 12 inches + 4 × Area of triangle having height 12 inches and base 20 inches,

$=5\times (12^2)+4\times ( \frac{1}{2}\times 10\times 12)$

$=5\times 144 + 4\times \frac{1}{2}\times 120$

$=720 + \frac{480}{2}$

$=720+240=960\text{ square inches}$

Hence, the surface area of the given pyramid is 960.

Answer 2

Answer:

960 square inches

Step-by-step explanation:

Given that he base of the figure shown is a cube with sides that are 12 inches long. the total height of the figure is 20 inches.

Surface area of pyramid = surface area of bottom cube exposed + surface area of 4 triangles on the top

Bottom cube has only 5 sides exposed

HEnce surface area of bottom = 5 (12x12) = 720

Area of each triangle top with base =12 and height = 10 is

1/2 bh = 1/2 (12)(10) = 60

Surface area of 4 triangles = 240

Total surface area = 720+240 =960 square inches