A square pyramid has a slant height of 13 meters and a height of 12 meters. What is the surface area if the square base has sides of length 10 meters?
360 m2
320 m2
260 m2
120 m2
Total area - area of base =
12,600 - 10,000 = 2600
http://easycalculation.com/area/pyramid.php
Typo somewhere
Oh, sorry, I used 100 and not 10 and 120 not 12
answer is 260 for sides without base
360 including base
To find the surface area of a square pyramid, you need to calculate the areas of its different faces and then add them up.
The square base of the pyramid has sides of length 10 meters. Therefore, the area of the base is 10 * 10 = 100 m^2.
The other faces of the pyramid are triangular faces, which will have the same area since the pyramid is a regular pyramid. The area of a triangle can be calculated using the formula: 1/2 * base * height.
The base of each triangle is the side length of the square base, which is 10 meters. The height of each triangle can be found using the Pythagorean theorem, since the slant height and height form a right triangle.
Using the Pythagorean theorem: slant height^2 = height^2 + base^2
Therefore, slant height^2 = 12^2 + 10^2 = 144 + 100 = 244
Taking the square root of both sides: slant height = √244 ≈ 15.62 meters
Now we can calculate the area of each triangular face:
Area of each triangular face = 1/2 * base * height = 1/2 * 10 * 15.62 ≈ 78.12 m^2
Since the pyramid has 4 triangular faces:
Total area of the triangular faces = 4 * 78.12 = 312.48 m^2
Finally, to find the surface area of the square pyramid, we add the area of the base to the total area of the triangular faces:
Surface area = area of base + total area of triangular faces = 100 + 312.48 = 412.48 m^2
Rounding to the nearest whole number, the surface area of the square pyramid is 412 m^2.
None of the provided options match the correct answer of 412 m^2.
To find the surface area of a square pyramid, we need to calculate the areas of each of its components and add them together.
First, let's find the area of the square base. The formula to find the area of a square is side length squared. Since the square base has sides of length 10 meters, the area of the square base is 10^2 = 100 square meters.
Next, let's find the area of the four triangular faces. Each face is a right triangle with a base length equal to the side length of the square base and a height equal to the slant height of the pyramid. The formula to find the area of a triangle is 1/2 * base * height.
The base length of each triangular face is 10 meters, and the height is 13 meters. So, the area of each triangular face is 1/2 * 10 * 13 = 65 square meters.
Since the pyramid has four triangular faces, the total combined area of the triangular faces is 4 * 65 = 260 square meters.
Finally, to find the total surface area of the pyramid, we add the area of the base and the area of the triangular faces: 100 + 260 = 360 square meters.
Therefore, the correct answer is 360 m2.