Question

Find the surface area of the regular pyramid shown to the nearest whole number.

Answer 1

Will you help me solve that

Answer 2

To find the area of the base use this formula....

\(\Huge{A=\frac{1}{2}(a \times p)}\)

In which a is the apothem and p is the perimeter....

Which is the apothem and what is the perimeter?

Answer 3

I am not sure

Answer 4

Look at pic below....

Answer 5

72

Answer 6

Correct ^^

Now we would input the perimeter and the apothem into the equation and solve....

\(\Huge{A=\frac{1}{2}(6\sqrt{3} \times 72)}\)

First solve \(\LARGE{(6 \sqrt{3} \times 72)}\) What would that equal?

Answer 7

10.39

Answer 8

for the first part?

Answer 9

Not quite. When multiplying with radicals we would multiply with the outside number ^^

\(\Huge{6 \times 72 \sqrt{3} \rightarrow 432\sqrt{3}}\)

Now we would divide by 2 in which we would only do with the outside number....

\(\Huge{\frac{432}{2} \sqrt{3}\rightarrow~ ?}\)

What would that equal?

Answer 10

374.12

Answer 11

Correct ^^

Now we need to find the Lateral Area.... So to find that we would use this formula...

\(\Huge{L.A=\frac{1}{2} ~perimeter \times h}\)

Where h is the slant height...now what is the slant height and the perimeter?

Answer 12

2057.66

Answer 13

That seems a bit to large...

The perimeter is 72 from before and the slant height is 11 in which we would input....

\(\Huge{L.A=\frac{1}{2} (72 \times 11)}\)

What would that equal?

Answer 14

396

Answer 15

Correct ^^ Now we would add the area of the base and the lateral area to find the Surface area of the pyramid...

\(\Huge{S.A=396 + 374.12}\)

Answer 16

770

Answer 17

Yup :)