A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 12 inches long, and the height of the equilateral triangle is 10.4 inches. The pyramid's slant height is 8 inches. What is its surface area?
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 6 millimeters long, and the height of the equilateral triangle is 5.2 millimeters. The pyramid's slant height is 6 millimeters. What is its surface area?
To find the surface area of the triangular pyramid, we need to sum the areas of the four triangular faces.
First, we calculate the area of the equilateral triangular base. The formula for the area of an equilateral triangle is given by:
A = (sqrt(3)/4) * s^2, where A is the area and s is the side length of the triangle.
Given that the side length of the equilateral triangle is 12 inches, we can substitute it into the formula:
A_base = (sqrt(3)/4) * (12^2)
Next, we calculate the area of the three identical lateral faces. Each lateral face is an isosceles triangle, with the slant height as the hypotenuse, the height of the equilateral triangle as one of the legs, and the side length of the equilateral triangle as the base.
The formula for the area of an isosceles triangle is given by:
A_lateral = (1/2) * b * h, where A_lateral is the area, b is the base, and h is the height.
Given that the base of each isosceles triangle is 12 inches and the height is 10.4 inches, we can substitute these values into the formula:
A_lateral = (1/2) * 12 * 10.4
Finally, we calculate the surface area of the triangular pyramid by summing the areas of the base and the three lateral faces:
Surface area = A_base + 3 * A_lateral
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please give the answer
the correct one
base: 1/4 * 12^2 * √3 = 36√3
each face: 1/2 * 12 * 8 = 48
Now finish it off