203k views
4 votes
Rachel has a toy shaped like a triangular pyramid in which the base and the lateral faces are congruent equilateral triangles. The side lengths of the triangles are 4 inches. The height of each triangle is about 3.5 inches. Rachel wants to cover all the lateral surfaces except for the base with yellow paper.

The amount of paper required to cover the lateral surfaces is about
square inches. If she wants to cover the entire pyramid with yellow paper, she would require about
more square inches of paper.

2 Answers

6 votes

Answer:

21 and 7

Explanation:

have a good day

User Palpatim
by
3.5k points
3 votes

Answer:

  • 21 square inches for lateral area
  • 7 more square inches for the base

Explanation:

The regular tetrahedron Rachel wants to cover has four congruent triangular faces, each with a base of 4 inches and a height of 3.5 inches. The area of each face is given by the triangle area formula:

A = 1/2bh

Rachel's toy has triangular faces with an area of ...

A = 1/2(4 in)(3.5 in) = 7.0 in²

__

Lateral Surfaces

The lateral surfaces consist of 3 of these triangles, so will have a total area of ...

3 × 7.0 in² = 21 in²

Paper to cover the lateral surfaces is about 21 square inches.

__

Base

The base is congruent to the other sides, so will have the same area they do. To cover the base, Rachel need ...

about 7.0 more square inches

Rachel has a toy shaped like a triangular pyramid in which the base and the lateral-example-1
User Popcorny
by
3.9k points