Question

Here is a triangular pyramid and its net.

The lateral faces are congruent triangles. The base (shaded) is an equilateral triangle.
(All lengths are in millimeters.)

Answer 1

Sample answer A triangular pyramid with an equilateral triangle for a base has four faces the equilateral triangular base and

three congruent isosceles triangular faces

Explanation:

Answer 2

a) Area of the base of the pyramid =
`15.6\ mm^(2)`

b) Area of one lateral face =
`24\ mm^(2)`

c) Lateral Surface Area =
`72\ mm^(2)`

d) Total Surface Area =
`87.6\ mm^(2)`

Explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle.
`\text{Area of triangle = } (1)/(2) * \text{Base} * \text{Height} ..... (1)\\`

`{\Rightarrow \text{Area of pyramid's base = }(1)/(2) * 6 * 5.2\\\Rightarrow 15.6\ mm^(2)`

b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

`\Rightarrow (1)/(2) * 8 * 6\\\Rightarrow 24\ mm^(2)`

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

`\text{Lateral Surface Area = }3 * \text{ Area of one lateral surface}\\\Rightarrow 3 * 24 = 72 mm^(2)`

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to Lateral Surface Area + Area of base

`\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\ mm^(2)`

Hence,

a) Area of the base of the pyramid =
`15.6\ mm^(2)`

b) Area of one lateral face =
`24\ mm^(2)`

c) Lateral Surface Area =
`72\ mm^(2)`

d) Total Surface Area =
`87.6\ mm^(2)`