A square pyramid has base edge length 14 m. The height of the pyramid is 24 m. Find the surface area of the square pyramid. Use pencil and paper. Draw a net for the figure and find the surface area.
Each face of the pyramid is a triangle with base 14.
If you draw the net, things get easy. You have a square and four triangles.
Draw a line from the vertex to the center of an edge of the base.
You now have a right triangle with sides 7,24,25.
That is, each triangular face has altitude 25.
So, the area of the pyramid is
14^2 + 4(14*25/2)
To find the surface area of a square pyramid with a given base edge length and height, we can break it down into the surface area of the base and the surface area of the four triangular faces.
1. Surface area of the base:
The base of the square pyramid is a square, so the area of the base is given by the formula: Area = side^2.
Given that the base edge length is 14 m, the area of the base is: Area = 14^2 = 196 square meters.
2. Surface area of the four triangular faces:
Each triangular face of the pyramid is an isosceles triangle, with two sides of length 14 m (the base of the square) and one side of height 24 m (the slant height). We can use the formula for the area of an isosceles triangle: Area = 0.5 x base x height.
Given that the base length is 14 m and the height (slant height) is 24 m, the area of each triangular face is: Area = 0.5 x 14 x 24 = 168 square meters.
Since there are four triangular faces, the total surface area of these faces is: 4 x 168 = 672 square meters.
3. Total surface area:
Finally, to find the total surface area of the square pyramid, we add the surface area of the base and the surface area of the four triangular faces:
Total surface area = base area + triangular face areas = 196 + 672 = 868 square meters.
Now, let's draw a net of the figure to visualize its faces and find the surface area.
First, draw a square for the base with side length 14 m. Label the corners as A, B, C, and D.
Join the four corners of the base to the apex of the pyramid. Label these edges as AE, BE, CE, and DE.
Now, you have the net of the square pyramid.
Calculate the area of each face (the base and the four triangles) and add them together to find the surface area, which we've already determined to be 868 square meters.
To find the surface area of a square pyramid, we need to calculate the areas of the individual faces and then sum them together.
First, let's draw a net for the square pyramid. A net is a two-dimensional representation of a three-dimensional shape that can be cut out and folded to create the shape.
For a square pyramid, the net consists of a square base and four triangular faces.
To draw the net:
1. Draw a square with edge length 14 m for the base.
2. Draw four triangles with a common vertex at the top of the square, connecting each corner of the base with the top vertex.
Next, we need to calculate the areas of each face.
The base of the pyramid is a square with edge length 14 m, so its area is 14^2 = 196 square meters.
The four triangular faces are all congruent, so we just need to calculate the area of one of them and multiply by 4.
To find the area of a triangle, we need the base length and height. In this case, the base of the triangle is also 14 m (since each side of the square base is the same length), and the height of the pyramid is given as 24 m.
The formula for the area of a triangle is: Area = (1/2) * base * height
So, the area of one triangular face is (1/2) * 14 * 24 = 168 square meters.
Since there are four triangular faces, the total area of all the triangular faces is 4 * 168 = 672 square meters.
Finally, we can find the total surface area by adding the areas of the base and the triangular faces: 196 + 672 = 868 square meters.
Therefore, the surface area of the square pyramid is 868 square meters.