Please help I'm very confused
Find the lateral area of a square pyramid. Base: 8, Height: 22, and side: 8
Please
I'm confused too: Base: 8, Height: 22, and side: 8 ?
Do you mean a square base with side 8?
If so, draw a side view. The altitude from the vertex to the base lands in the center of the square, 4 units from each side. Then the slant height can be found using
s^2 = 4^2+22^2
s = 10√5
The lateral area is just the areas of the four slanting triangular sides, each with base 8 and height s. So,
area = 4 * (8*10√5)/2 = 160√5
To find the lateral area of a square pyramid, you need to know the length of the base and the slant height.
Given:
Base length (s) = 8
Height (h) = 22
To find the slant height (l) of the pyramid, we can use the Pythagorean theorem.
Using the base length and height, we have:
l^2 = (s/2)^2 + h^2
l^2 = (8/2)^2 + 22^2
l^2 = 4^2 + 22^2
l^2 = 16 + 484
l^2 = 500
l = √500
l ≈ 22.36
Now that we have the slant height, we can find the lateral area.
Lateral area = (s * l) / 2
Lateral area = (8 * 22.36) / 2
Lateral area = 178.88
Therefore, the lateral area of the square pyramid is approximately 178.88 square units.
To find the lateral area of a square pyramid, you need to calculate the sum of the areas of all the lateral faces.
In this case, the base of the square pyramid has a side length of 8. So, the area of the base can be found by squaring the side length: 8 x 8 = 64 square units.
The lateral faces of a square pyramid are triangles. Each lateral face is an isosceles triangle, with two congruent sides (the edges of the square base) and a height equal to the slant height of the pyramid.
To find the slant height, you can use the Pythagorean theorem. The slant height (l) of each triangular face of the pyramid can be calculated as follows:
l^2 = h^2 + s^2
where h is the height of the pyramid and s is the side length of the base.
In this case, the height (h) of the pyramid is given as 22, and the side length of the base (s) is given as 8. Plugging these values into the equation, we have:
l^2 = 22^2 + 8^2
l^2 = 484 + 64
l^2 = 548
l ≈ 23.4 (rounded to one decimal place)
Now that we have the slant height, we can calculate the area of each lateral face (triangle) using the formula:
A = 0.5 x base x height
In this case, the base and height of each lateral face are both equal to the side length of the base (8 units). So the area of each lateral face is:
A = 0.5 x 8 x 8
A = 32 square units
Finally, to find the lateral area of the pyramid, we need to find the sum of the areas of all the lateral faces. Since a square pyramid has four lateral faces, the total lateral area is:
Lateral Area = 4 x Area of each lateral face
Lateral Area = 4 x 32
Lateral Area = 128 square units.
Therefore, the lateral area of the square pyramid with a base length of 8, height of 22, and side length of 8 is 128 square units.