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 7. How much fabric will Keivan need to construct his tent?Responses
To calculate the total fabric needed, we first need to determine the surface area of each base and each rectangle.
Surface area of an equilateral triangle with side length 5:
A = (sqrt(3) / 4) * s^2
A = (sqrt(3) / 4) * 5^2
A = (sqrt(3) / 4) * 25
A = (1.732 / 4) * 25
A = 4.33 * 25
A = 108.25 square units
Surface area of a rectangle with length 7 and width 5:
A = l * w
A = 7 * 5
A = 35 square units
Total fabric needed for the tent:
2 bases = 2 * 108.25 = 216.5 square units
3 rectangles = 3 * 35 = 105 square units
Total fabric needed = 216.5 + 105 = 321.5 square units
Therefore, Keivan will need 321.5 square units of fabric to construct his tent.