A square pyramid has a base of 13mm and a slant height of 9mm, what is it's surface area?
Well, a square pyramid is like a pyramid that had a little too much to eat, and now it has a square base instead of a triangle. Now, to find the surface area of this chubby pyramid, we need to take into account the base and the 4 triangular faces.
First, let's calculate the area of the base. Since it's a square, we can simply square the length of one side. So, 13mm squared gives us 169mm².
Now, for the 4 triangular faces, we need to use the slant height and the base length. Each triangular face has a height equal to the slant height and a base equal to the length of one side of the square base.
Using the formula for the area of a triangle (Area = 0.5 * base * height), we can calculate the area of one triangular face: 0.5 * 13mm * 9mm = 58.5mm².
Since there are 4 triangular faces, we multiply the area of one by 4: 58.5mm² * 4 = 234mm².
Finally, we can add the area of the base and the 4 triangular faces together to get the total surface area: 169mm² + 234mm² = 403mm².
So, the surface area of this chubby square pyramid is 403mm².
To find the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces.
1. Calculate the area of the base:
The base of the square pyramid is a square, so its area is given by the formula: area = side^2.
In this case, the side length of the base is 13mm, so the area of the base is:
area_base = 13mm * 13mm = 169mm^2.
2. Calculate the area of a triangular face:
Each triangular face is an isosceles triangle with one side being the slant height (9mm), and the other two sides being equal to the base side length (13mm).
To find the area of an isosceles triangle, you can use the formula: area = (base * height) / 2.
The base of the triangle is 13mm, and the height can be found using the Pythagorean theorem:
height = sqrt(slant height^2 - (base/2)^2)
= sqrt(9mm^2 - (13mm/2)^2)
= sqrt(81mm^2 - 42.25mm^2)
= sqrt(38.75mm^2)
≈ 6.22mm.
Therefore, the area of each triangular face is:
area_triangle = (13mm * 6.22mm) / 2
≈ 40.43mm^2.
3. Calculate the total surface area:
The square pyramid has a base with area 169mm^2, and four triangular faces with total area 40.43mm^2 each.
So the total surface area is:
surface_area = area_base + 4 * area_triangle
= 169mm^2 + 4 * 40.43mm^2
= 169mm^2 + 161.72mm^2
= 330.72mm^2 (rounded to two decimal places).
Therefore, the surface area of the square pyramid is approximately 330.72mm^2.
To find the surface area of a square pyramid, you need to calculate the area of its base and the areas of its four triangular faces, and then sum them up.
First, let's calculate the area of the base. Since the base is square, the formula to find its area is:
Area of a square = side length x side length
In this case, the side length of the base is 13mm, so the area of the base is:
Area of base = 13mm x 13mm = 169mm²
Next, let's calculate the areas of the four triangular faces. Each triangular face is a right triangle with a base 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:
Area of a triangle = 1/2 x base x height
Since the base of each triangular face is 13mm and the height is 9mm, the area of each triangular face is:
Area of each triangular face = 1/2 x 13mm x 9mm = 58.5mm²
Since there are four triangular faces on a square pyramid, the total area of the triangular faces is:
Total area of triangular faces = 4 x 58.5mm² = 234mm²
Now, we can find the surface area by summing up the area of the base and the areas of the triangular faces:
Surface area = Area of base + Total area of triangular faces
= 169mm² + 234mm²
= 403mm²
Therefore, the surface area of the square pyramid is 403mm².
the surface area is the square base plus four triangles, so
A = 13^2 + 4(13*9/2) = _____ mm^2