Find the surface area of a square pyramid with a length of 5 cm and a slant height of 8 cm.
A.) 80 cm²
B.) 105 cm²
C.) 200 cm²
D.) 145 cm²
well the area of each triangular side is (1/2) * 5 * 8 = 20
4 sides so 80 cm^2 for the sides
Your question does not specify if the bottom is included in which case add 25 to 80 and get 105 cm^2
thank you!
You are amazing!
Sending an imaginary box of chocolates to you. Happy valentines day!
Thanks, but already over my wrestling weight :)
lol
Are you a teacher/monitor/helper on Questions LLC. Not trying to be a stalker but your profile says you've been on here, by how far I have looked, since 2014. You clearly are not a student.........most likely.
Retired professor of engineering, no association with LLC management although I was involved with similar help sites years ago.
To find the surface area of a square pyramid, we need to compute the area of each face and add them together.
First, let's calculate the base area of the square pyramid. Since the pyramid has a square base, we can use the formula A = s^2, where "s" represents the length of one side of the square base. In this case, the length is given as 5 cm, so the base area is calculated as 5^2 = 25 cm².
Next, we need to find the area of the four triangular faces. Each triangular face is a right triangle, and we can find the area of a triangle using the formula A = 1/2 * b * h, where "b" represents the base length and "h" represents the height of the triangle.
The base length of each triangular face is the same as the length of one side of the square base (5 cm). The height can be found using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the slant height of the pyramid (8 cm), and one of the other two sides is half the length of the base (2.5 cm). Thus, the height can be calculated as √(8^2 - 2.5^2) = √60.75 ≈ 7.80 cm.
Now, we can find the area of one triangular face by substituting the base length and height into the area formula: A = 1/2 * 5 cm * 7.80 cm ≈ 19.50 cm². Since there are four triangular faces, the total area of the triangular faces is 4 * 19.50 cm² = 78 cm².
Finally, we can find the total surface area of the square pyramid by adding the base area and the area of the triangular faces: 25 cm² + 78 cm² = 103 cm².
Therefore, the correct answer is not listed. The surface area of the given square pyramid is approximately 103 cm².