Ask Question
12 March, 00:08

To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then she glued the pyramids' bases together to form the gemstone. The surface area of the gemstone is 520 square inches. What is the value of x? Explain.

+2
Answers (1)
  1. 12 March, 03:01
    0
    8 inches.

    Step-by-step explanation:

    From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

    Ab = s ^ 2 = 100

    Therefore each side would be:

    s = (100) ^ (1/2)

    s = 10

    So, side of the square base = 10 inches

    Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

    Ap = 520/2 = 260

    For an area of the square pyramid we have the following equation:

    Ap = 2 * x * s + s ^ 2

    Where x is the height of each triangular surface and s is the side of the square base

    Replacing we have:

    260 = 2 * x * 10 + 10 ^ 2

    20 * x + 100 = 260

    20 * x = 160

    x = 160/20

    x = 8

    Therefore, the value of x is 8 inches.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then she glued ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers