Keivan wants to build a tent for his next camping trip. He determines that each base will be an equilateral triangle with side lengths of and a height of . The bases will be connected by rectangles with a length of . How much fabric will Keivan need to construct his tent?Responses

Answer 1

To calculate the amount of fabric needed to construct the tent, we need to find the total surface area of the tent.

First, let's find the area of each equilateral triangle base:
Area of equilateral triangle = (sqrt(3) / 4) x side^2
Area of each base = (sqrt(3) / 4) x 5^2 = (sqrt(3) / 4) x 25 = 21.65 square units

Next, let's find the area of each rectangle:
Area of rectangle = length x width
Area of each rectangle = 5 x 3 = 15 square units

Now, let's calculate the total surface area of the tent:
Total surface area = 2 x area of base + 3 x area of rectangle
Total surface area = 2 x 21.65 + 3 x 15
Total surface area = 43.3 + 45
Total surface area = 88.3 square units

Therefore, Keivan will need 88.3 square units of fabric to construct his tent.