Question

A triangular pyramid. The base has a base of 12 and height of 2.5. A triangular side has a base of 12 and height of 13.1, another side has a base of 6.5 and height of 14, and another side has a base of 6.5 and height of 14.

What is the lateral area of the triangular pyramid?

Answer 1

169.6 units²

Explanation:

Lateral surface area of a pyramid is the sum of all faces except the base

(½×12×13.1) + (½×6.5×15) + (½×6.5×14)

= 78.6 + 45.5 + 45.5

= 169.6

Answer 2

169.6 units squared

Explanation:

The lateral area is basically the surface area of the figure minus the base area.

Here, we just need to find the area of each triangular side and add those together. The triangles we have are:

1. Δ with base 12 and height 13.1

2. Δ with base 6.5 and height 14

3. Δ with base 6.5 and height 14

The area of a triangle is denoted by:
`A=(1)/(2) bh`, where b is the base and h is the height. The areas are thus:

1.
`A=(1)/(2) *12*13.1=78.6` units squared

2.
`A=(1)/(2) *6.5*14=45.5` units squared

3.
`A=(1)/(2) *6.5*14=45.5` unit squared

Add these together:

78.6 + 45.5 + 45.5 = 169.6 units squared