Question 13 (1 point) $\checkmark$ Saved
True or False. A pyramid has a slant height of $15 \mathrm{ft}$. and a square base with a perimeter of $72 \mathrm{ft}$. The pyramid has a lateral area of $880 \mathrm{ft}^{2}$.
Answer
Therefore, the statement that the pyramid has a lateral area of 880 \(\text{ft}^{2}\) is \(\boxed{\text{False}}\). The calculated lateral area of the pyramid is 540 square feet, which is not equal to the given lateral area of 880 square feet.
Step 1 ：Given that the pyramid has a slant height of 15 ft and a square base with a perimeter of 72 ft, we can calculate the lateral area using the formula \(\frac{1}{2} \times \text{perimeter of base} \times \text{slant height}\).
Step 2 ：Substituting the given values into the formula, we get \(\frac{1}{2} \times 72 \times 15 = 540 \, \text{ft}^{2}\).
Step 3 ：Comparing this with the given lateral area of 880 \(\text{ft}^{2}\), we see that they are not equal.
Step 4 ：Therefore, the statement that the pyramid has a lateral area of 880 \(\text{ft}^{2}\) is \(\boxed{\text{False}}\). The calculated lateral area of the pyramid is 540 square feet, which is not equal to the given lateral area of 880 square feet.
