To find the surface area of a pyramid, we need to find the area of each face and then add them together. The base of the pyramid is a regular triangle with side length 17m and height 8.5√3m. We can use the formula for the area of an equilateral triangle:
A = (sqrt(3)/4) * s^2
where s is the length of a side. Plugging in s = 17m, we get:
A = (sqrt(3)/4) * 17^2
A = 165.25m^2
This is the area of one face of the pyramid. There are four other faces, which are all triangles with base 17m and slant height 9m (the height of the pyramid). To find the height of these triangles, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the legs and c is the hypotenuse (slant height). Plugging in a = 8.5√3m and c = 9m, we get:
(8.5√3)^2 + b^2 = 9^2
72.25 + b^2 = 81
b^2 = 8.75
b ≈ 2.96m
So the height of each triangular face is approximately 2.96m. The area of each triangular face is:
A = (1/2) * base * height
A = (1/2) * 17m * 2.96m
A ≈ 25.16m^2
Adding up the areas of all five faces, we get:
165.25m^2 + 4(25.16m^2)
= 273.97m^2
To the nearest whole number, the surface area of the pyramid is 274m^2.
Find the surface area of the regular pyramid shown to the nearest whole number the figure is not drawn to scale
17m
8.5 √3m ---
9m
1 answer