Mathematics, 09.07.2019 19:20 garrettrhoad

Aright pyramid with a square base has a base edge length of 12 meters and slant height of 6 meters.
the apothem is meters.
the hypotenuse of δabc is the .
the height is meters.
the volume of the pyramid is cubic meters.

Aright pyramid with a square base has a base edge length of 12 meters and slant height of 6 meters.<

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Answer from: FAKE5979

Correct responses:

The apothem is 6 metersThe hypotenuse of ΔABC is 6·√2 metersThe height is 6 meterThe volume of the pyramid is 288 cubic metersMethods used for the calculations

The given dimensions of the right pyramid having a square base are;

Base edge length, l = 12 meters

Slant height = 6·√3

Required:

Length of the apothem.

Solution:

The apothem, a, is the line drawn from the middle of the polygon to the midpoint of a side.

Therefore;

The apothem of the square base = $\dfrac{l}{2}$ = $\overline{BC}$

Which gives;

$a = \dfrac{12}{2} = 6$

The apothem is 6 meters

Required:

The hypotenuse of triangle ΔABC

Solution:

The hypotenuse of ΔABC = The slant height of the square pyramid = 6·√2 meters

Therefore;

The hypotenuse of ΔABC = 6·√2 meters

Required:

The height of the pyramid

Solution:

The height of the pyramid = The length of the side $\overline{AC}$ in right triangle

ΔABC, therefore, by Pythagorean theorem, we have;

$\overline{AC}^2$ = $\overline{AB}^2$ - $\overline{BC}^2$

Which gives;

$\overline{AC}^2$ = (6·√2)² - 6² = 6²·((√2)² - 1) = 6² × 1 = 6²

$\overline{AC}$ = √(6²) = 6

The height of the pyramid, h = $\overline{AC}$ = 6 meters

Required:

The volume of the pyramid.

Solution:

$The \ volume \ of \ a \ pyramid \ is, \ V = \mathbf{\dfrac{1}{3} \times Base \ area \times Height}$

$V = \dfrac{1}{3} \times A \times h$

The base area of the square pyramid, A = 12 m × 12 m = 144 m²

Therefore;

$V = \dfrac{1}{3} \times 144\, m^2 \times 6 \, m = 288 \, m^2$

The volume of the pyramid is V = 288 cubic meters

Learn more about the volume of solids here:

link

Answer from: Emmarazek

Step-by-step explanation:

Square base of the base edge = 12 meters and slant height = 6√2 meters

Apothem of the right pyramid will be = AC

1). Now AC = $\sqrt{AB^{2}-BC^{2}}$

AC = $\sqrt{(6\sqrt{2})^{2}-(6)^{2}}$

= $\sqrt{72-36}=\sqrt{36}$

= 6

Now Apothem = 6 meters

2). Hypotenuse of Δ ABC = AB = 6√2 meters

3). Height AC = 6 meters

4). Volume of the pyramid = $\frac{1}{3}(\text{Area of the base})(\text{Apothem})$

Volume = $\frac{1}{3}(12)^{2}(6)$

= 2×144

= 288 meter²

Answer from: Quest

0.32

step-by-step explanation:

2.24/7

Answer from: Quest

6mm^3 or .6cm^3

216

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36 6

/ \ /

6 6 6

factor trees are nice.

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Aright pyramid with a square base has a base edge length of 12 meters and slant height of 6 meters.<...