Mathematics, 16.10.2019 03:50 Knownothing

For a project, gabrielle made a model of an egyptian pyramid. the square base has a side length measuring 10 inches. the pyramid is 12 inches tall.
what is the surface area of the model?

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Answer from: Brock2002

The surface area of the model is 360 inches².

By identifying that you're working with a square pyramid, you can interpret that the square base has 4 equal sides. Since the question only provides you with the side length of the square base and the height of the pyramid, you would need to find the slant height of the triangles in order to find the surface area. Since the pyramid is square, the height (line from the top vertex of the pyramid to the center of the square) should be perpendicular to the square. You can interpret that to be a right triangle with in the pyramid. Since the height line is in the center of the square, you would need to take the side length of the square base and divide it in half in order to get a side component for the Pythagoras theorem needed to find the slant height. (10/2 = 5). With that, you plug the components (pyramid height and side length/2) into the Pythagoras theorem (a² + b² = c²).

12² + 5² = c²
144 + 25 = 169
√169 = 13

The slant height is 13. You take that component and multiply it with the side length, then divide it by 2, in order to find the area of the triangle that makes up the pyramid. You then take that product and multiply it by 4 to find the lateral area.

13 x 10 = 130
130/2 = 65
65 x 4 = 260
LA = 260

To find the total surface area, you add the lateral area (260) with the base area (the square).

260 + (10 x 10)
SA = 360

Attached is a diagram to help you visualize the problem.

Hope this helps!

For a project, gabrielle made a model of an egyptian pyramid. the square base has a side length meas

For a project, gabrielle made a model of an egyptian pyramid. the square base has a side length meas

Answer from: Quest

Many things that seem threatening in the dark become welcoming when we shine light on them

Answer from: Quest

Hello!

the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

$\frac{a^{m} }{a^{n} }=a^{m-n}$

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

$\frac{3^{4} }{3^{1}}$

then, calculating we have:

$\frac{3^{4} }{3^{1}}=3^{4-1}=3^{3}$

hence, the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

have a nice day!

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