A triangular pyramid has faces that are all equalatetal triangles. Each side length is 16 cm. What is the surface area of the pyramid?
So you have a tetrahedron
area of one of the triangles
= (1/2)(16)(16)sin60
= 128(√3/2) = 64√3
Counting the base there are 4 faces, so
surface area = 4(64√3) = 256√3 = appr 443.4 cm^2
If you don't want to count the base, multiply by 3 instead of by 4
four sides, area=4(1/2 b h)
but you can find h from
tan60=h/(b/2) or h=base*tan60 /2
area=2(bh)=2(b*b*tan60/2)=b^2 tan60
check my math.
To find the surface area of a triangular pyramid, we need to calculate the area of each triangular face and then sum them up.
Since the pyramid has equilateral triangles as faces, we can use the formula for the area of an equilateral triangle, which is (sqrt(3) / 4) * side^2.
In this case, the side length is given as 16 cm.
Let's calculate the area of one triangular face:
Area of an equilateral triangle = (sqrt(3) / 4) * side^2
= (sqrt(3) / 4) * 16^2
= (sqrt(3) / 4) * 256
= 64 * sqrt(3)
Since the pyramid has 4 faces, we need to multiply the area of one face by 4 to get the total surface area:
Total surface area of the pyramid = Area of one face * 4
= 64 * sqrt(3) * 4
= 256 * sqrt(3) cm^2
Therefore, the surface area of the given triangular pyramid is 256 * sqrt(3) square centimeters.