Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Surface Areas of Pyramids 
> Section Exercises 
8.3 > Exercise 19
quare pyramid has four congruent triangular faces. The slant height of each face is 7 centimeters. The lateral surface area of the pyramid is 122 square centimeters. Find the th ace area of the pyramid.

Surface Areas of Pyramids > > Section Exercises 8.3> 8.3> Exercise 1919\newlinequare pyramid has four congruent triangular faces. The slant height of each face is 77 centimeters. The lateral surface area of the pyramid is 122122 square centimeters. Find the th ace area of the pyramid.

Full solution

Q. Surface Areas of Pyramids > > Section Exercises 8.3> 8.3> Exercise 1919\newlinequare pyramid has four congruent triangular faces. The slant height of each face is 77 centimeters. The lateral surface area of the pyramid is 122122 square centimeters. Find the th ace area of the pyramid.
  1. Find Perimeter of Base: First, we need to find the perimeter of the base of the pyramid. Since the lateral surface area (LSA) is the sum of the areas of the four triangular faces, we can find the area of one triangle and then the base length of that triangle.\newlineLSA = 4×(12×base×slant height)4 \times (\frac{1}{2} \times \text{base} \times \text{slant height})\newline122=4×(12×base×7)122 = 4 \times (\frac{1}{2} \times \text{base} \times 7)
  2. Calculate Area of Triangle: Now, let's solve for the base.\newline122=2×base×7122 = 2 \times \text{base} \times 7\newlinebase=1222×7\text{base} = \frac{122}{2 \times 7}\newlinebase=12214\text{base} = \frac{122}{14}\newlinebase=8.71\text{base} = 8.71, but this seems off because the base should be a whole number if we're dealing with a pyramid in a typical math problem. Let's check the calculation again.

More problems from Evaluate variable expressions: word problems