Question

Consider the triangular pyramids shown.

Pyramid 1
Pyramid 2

Pyramid 1 is a triangular pyramid. The base has a base of 12 and height of 2.5. A side has a base of 12 and height of 13.1. 2 sides have a base of 6.5 and height of 14.
[Not drawn to scale]

Pyramid 2 is a triangular pyramid. The base has a base of 12 and height of 4.5. A side has a base of 12 and height of 6.5. 2 sides have a base of 7.5 and height of 8.
[Not drawn to scale]

The base of each pyramid is an isosceles triangle. Which has the greater surface area?
Pyramid 1 is greater by 58.6 square units.
Pyramid 1 is greater by 70.6 square units.
Pyramid 2 is greater by 12 square units.
Pyramid 2 is greater by 24 square units.

Answer 1

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Answer:

(a) Pyramid 1 by 58.6 square units

Explanation:

The area of each triangle is given by the formula ...

A = 1/2bh

The total area is the area of all four triangles that make up the outer surface of the pyramid.

Pyramid 1

A = 1/2(12×2.5 +12×13.1 +2(6.5×14)) = 184.6 . . . square units

Pyramid 2

A = 1/2(12×4.5 +12×6.5 +2(7.5×8)) = 126 . . . square units

Pyramid 1 has the larger area by ...

184.6 -126 = 58.6 . . . square units