Find the total surface area of a square pyramid with a base length of 18 and height of 12
the surface area of a prism is 120 sqaure cm and the area of each base is 32 square cm find the lateral area of the prism.
To find the total surface area of a square pyramid, you need to calculate the area of each face and then sum them up.
A square pyramid has a square base, so the base has an area of side length squared. In this case, the base length is 18, so the area of the base is 18^2 = 324.
The lateral faces of a square pyramid are triangles. The formula to calculate the area of a triangle is (base * height) / 2. In this case, the base of each lateral face is equal to the base length of the square pyramid, which is 18. The height of each lateral face can be calculated using the Pythagorean theorem, which gives us the slant height (l) of the pyramid.
To find the slant height, we can use the formula l = √(h^2 + (s/2)^2), where h is the height of the pyramid and s is the base length of the triangle.
Plugging in the values, we have l = √(12^2 + (18/2)^2) = √(144 + 81) = √225 = 15.
Now that we have the slant height, we can calculate the area of each lateral face using the formula (base * height) / 2. In this case, the base length is 18 and the height is 15.
Area of each lateral face = (18 * 15) / 2 = 270 / 2 = 135.
Since there are 4 lateral faces, the total area of the lateral faces is 4 * 135 = 540.
To find the total surface area, we need to add the area of the base to the area of the lateral faces.
Total Surface Area = Base Area + Lateral Faces Area = 324 + 540 = 864.
Therefore, the total surface area of the square pyramid with a base length of 18 and height of 12 is 864 square units.
What are the units that go with your numbers? Meters? Miles? Whetever?
The base area is 18x18 whatevers.
You need the lateral height h of the four triangular sides, measured from the midpoint of one of the base sides to the apex. You can get that using the Pythagorean theorem.
h^2 = 9^2 + 12^2
h = 15
One Side area = (1/2)bh = (1/2)*12*15 = 90
Add up the five side areas for the total.