Problem of the Week - Algebra and Up - March 28, 2021 to April 3, 2021

Algebra and Up: 

Question: A triangular prism-shaped tent has a rectangular base that is 6 feet wide and 8 feet long. The isosceles triangular sides have bases that are 6 feet wide and edges that are 5 feet in length. If all the walls of the tent are pulled perfectly flat, then what is the volume of the tent? 

Answer: 96 cubic feet

Solution: We are missing the height of the tent. To find it, we can take a right triangular half of an isosceles triangular side of the tent. One leg is half of 6 feet, so 3 feet, and the hypotenuse is 5 feet, so the other leg - the height of the tent - is 4 feet. So, the area of that face of the tent is 0.5 x 6 x 4 = 12 square feet. The length of the tent is 8 feet, so its total volume is 12 x 8 = 96 cubic feet.