What is the total surface area of a regular square pyramid with a base side length of 18cm and a height of 12cm?
the slant height is 15, so you have 4 triangles of base 18 and height 15
plus an 18x18 base if you want to include that.
To find the total surface area of a regular square pyramid, we need to find the sum of the areas of all its faces.
A regular square pyramid has a square base and four triangular faces. Let's calculate the areas of each face and then add them together.
1. Base: The base of the pyramid is a square. The formula to calculate the area of a square is A = s^2, where "s" is the length of a side. In this case, the side length of the base is 18 cm, so the area of the base is A = 18^2 = 324 square cm.
2. Triangular faces: Each triangular face is an isosceles right triangle. Since it is an isosceles triangle, the two shorter sides of the triangle are equal. The base of this triangle is the same as the side length of the square base, which is 18 cm. The height of the triangle is the height of the pyramid, which is 12 cm. The formula to calculate the area of a triangle is A = (1/2) * base * height. Therefore, the area of each triangular face is A = (1/2) * 18 cm * 12 cm = 108 square cm.
Now, let's calculate the total surface area by adding the areas of all the faces:
Total surface area = Base area + 4 × Face area
Total surface area = 324 square cm + 4 × 108 square cm
Total surface area = 324 square cm + 432 square cm
Total surface area = 756 square cm
Therefore, the total surface area of a regular square pyramid with a base side length of 18 cm and a height of 12 cm is 756 square cm.
To find the total surface area of a regular square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
1. Area of the base:
Since the base of the pyramid is a square, we can find its area by squaring the length of one of its sides. In this case, the base side length is 18 cm, so the area of the base is (18 cm)².
Area of the base = (18 cm)²
2. Area of the triangular faces:
The triangular faces of a regular square pyramid are all congruent, meaning they have the same dimensions. To find the area of one triangular face, we'll use the formula: Area = 0.5 * base * height.
In this case, the base of the triangle is the base side length of the pyramid, which is 18 cm. And the height of the triangle is the height of the pyramid, which is 12 cm.
Area of one triangular face = 0.5 * 18 cm * 12 cm
3. Total surface area:
To find the total surface area, we add up the area of the base and the areas of the four triangular faces.
Total surface area = Area of the base + (Area of one triangular face * 4)
Total surface area = (18 cm)² + (0.5 * 18 cm * 12 cm * 4)
Now, let's calculate the total surface area.
Total surface area = (18 cm)² + (0.5 * 18 cm * 12 cm * 4)