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:

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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

A)26•2=52there are 2 sides with the same length116-52=64the other 2 side have to be half of 64 each64/2=32the width is 32b)make two sentences about these steps because your teacher knows how you write and explain things.

Answer from: Quest

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.

Need , 5. find the perimeter. a. 40x – 10 b. 12x – 5 c. 20x – 5 d. 20x – 3

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