To calculate the total amount of fabric Keivan will need to construct his tent, we first need to find the surface area of each component (2 triangles and 3 rectangles).
Surface area of an equilateral triangle can be calculated using the formula:
A = (sqrt(3) / 4) * s^2
where s is the side length of the triangle.
Given that each side length is 4, the surface area of one triangle will be:
A = (sqrt(3) / 4) * 4^2
A = (sqrt(3) / 4) * 16
A = 4sqrt(3) square units
Since we have two triangles, the total surface area of the triangles will be:
Total triangle area = 2 * 4sqrt(3) = 8sqrt(3) square units
Now, let's calculate the surface area of the rectangles. The formula for the surface area of a rectangle is:
A = length * width
Given that the length is 7 and the height is 2.8, the surface area of one rectangle will be:
A = 7 * 2.8
A = 19.6 square units
Since there are 3 rectangles, the total surface area of the rectangles will be:
Total rectangle area = 3 * 19.6 = 58.8 square units
Adding the total surface area of the triangles and rectangles, we get:
Total fabric needed = Total triangle area + Total rectangle area
Total fabric needed = 8sqrt(3) + 58.8
Total fabric needed ≈ 79.15 square units
Therefore, Keivan will need approximately 79.15 square units of fabric to construct his tent.
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 4 and a height of 2.8. The bases will be connected by rectangles with a length of 7. How much fabric will Keivan need to construct his tent?Responses
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