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?
What is the surface area of the model?
2 answers:
The surface area of the model is 360 inches<span>².
</span>
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 (a<span>² + b</span><span>² = c</span><span>²).
</span>
12² + 5² = c<span>²
</span>144 + 25 = 169
<span>√169 = 13
</span>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!
</span>
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 (a<span>² + b</span><span>² = c</span><span>²).
</span>
12² + 5² = c<span>²
</span>144 + 25 = 169
<span>√169 = 13
</span>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!
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Answer:
Step-by-step explanation:
Since, By the given diagram,
The side of the inner square = Distance between the points (0,b) and (a-b,0)
Thus the area of the inner square = (side)²
Now, the side of the outer square = Distance between the points (0,0) and (a,0),
Thus, the area of the outer square = (side)²
Hence, the ratio of the area of the inner square to the area of the outer square