MATH SOLVE

3 months ago

Q:
# Pyramid ABCDE is a square pyramid.What is the lateral area of pyramid ABCDE ?49√3 mm²98√3 mm²196√3 mm²392√3 mm²

Accepted Solution

A:

Answer: Choice B, 98*sqrt(3)

-----------------------------------------

Explanation:

See the attached image. In that diagram, I'm focusing on triangle ABC which is one of the lateral sides. I've added h to the diagram which is the unknown slant height along the dashed line. I've also added point F which is directly under point A and also on segment BC.

Triangle AFC is a 30-60-90 triangle

Side FA = h is the unknown longer leg

The known shorter leg is FC = 7 since it is half of CB = 14

By using the 30-60-90 triangle template, we know that

longer leg = (shorter leg)*sqrt(3)

longer leg = 7*sqrt(3)

FA = 7*sqrt(3)

h = 7*sqrt(3)

Which means the area of triangle ABC is

area = (base*height)/2

area = (FC*FA)/2

area = (7*h)/2

area = (7*7*sqrt(3))/2

area = (49*sqrt(3))/2

that is the area of one triangle. But there are four of these triangles, so we multiply that result by 4

4*area = 4*(49*sqrt(3))/2 = 98*sqrt(3) which is the answer

note: the base is the square BCDE. The lateral sides are everything that isn't the base (so all of the triangles)

-----------------------------------------

Explanation:

See the attached image. In that diagram, I'm focusing on triangle ABC which is one of the lateral sides. I've added h to the diagram which is the unknown slant height along the dashed line. I've also added point F which is directly under point A and also on segment BC.

Triangle AFC is a 30-60-90 triangle

Side FA = h is the unknown longer leg

The known shorter leg is FC = 7 since it is half of CB = 14

By using the 30-60-90 triangle template, we know that

longer leg = (shorter leg)*sqrt(3)

longer leg = 7*sqrt(3)

FA = 7*sqrt(3)

h = 7*sqrt(3)

Which means the area of triangle ABC is

area = (base*height)/2

area = (FC*FA)/2

area = (7*h)/2

area = (7*7*sqrt(3))/2

area = (49*sqrt(3))/2

that is the area of one triangle. But there are four of these triangles, so we multiply that result by 4

4*area = 4*(49*sqrt(3))/2 = 98*sqrt(3) which is the answer

note: the base is the square BCDE. The lateral sides are everything that isn't the base (so all of the triangles)