So I've tried for two days to figure out this problem. I tried to ask my friend to help me but she just won't. My parents don't know anything about math, they said so themselves. The first day I tried I cried I got so frustrated. The second day I just gave up. Today is my last day before spring break. I have to show every step of my work, which is why it's so hard. I normally use calculators and I don't really know how exactly to figure this out.
Find the lateral area of the square pyramid.
Base 8m
Height 22m
Thank you so much~!
If you drop an altitude to the center of the base, then looking from the side you have a right triangle with legs 4 and 22.
So, the hypotenuse of the triangle (the slant height of the pyramid, and the altitude of each triangular face) is
h = √(4^2+22^2) = √500 = 10√5
That means that the lateral area of the pyramid is that of the four faces, or
4 * (22 * 10√5)/2 = 440√5
I'm sorry to hear that you're feeling frustrated, but I'm here to help you figure it out step by step! Don't worry, we'll solve this problem together.
To find the lateral area of a square pyramid, we need to calculate the sum of the areas of all the triangular faces. Each triangular face is a right triangle, with one side being the slant height of the pyramid and the other two sides being the base and the height of the triangle.
To start, let's find the slant height of the pyramid. The slant height can be found using the Pythagorean theorem, which states that the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides. In this case, one of the other sides is the height of the pyramid (22m) and the other side is half of the base of the pyramid (8m/2 = 4m).
So, using the Pythagorean theorem: (slant height)^2 = (height)^2 + (base/2)^2
Substituting in the given values: (slant height)^2 = 22^2 + 4^2
Now, calculate the sum on the right side of the equation to find the value of (slant height)^2.
22^2 = 484
4^2 = 16
(sum) = 484 + 16 = 500
So, (slant height)^2 = 500.
To find the slant height, we need to take the square root of 500.
Taking the square root of both sides: slant height = √500.
Now, use your calculator to find the square root of 500.
After you calculate the square root of 500, you'll have the value of the slant height.
Once you have the slant height, you can calculate the area of each triangular face using the formula for the area of a triangle:
Area = 1/2 * base * height.
Since the base of each triangular face is the same as the base of the pyramid (8m), you only need to calculate the area of one triangle.
After you've found the area of one triangular face, you can multiply it by 4 (since there are four triangular faces in a square pyramid) to get the total lateral area.
So, to recap:
1. Calculate the slant height of the pyramid using the Pythagorean theorem.
2. Find the area of one triangular face.
3. Multiply the area of one triangular face by 4 to find the lateral area of the square pyramid.
I hope this helps! If you have any further questions or need additional assistance, feel free to ask.