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.

Step-by-step explanation:

The lateral area that Rachel needs to cover is 21 inches squared. You find this by first finding the area of one triangular side. To do this, you must half the base of one side, so it makes 2, and multiply it by the height, which gets you to 7. Then, you must half this, as the formula for the area of a triangle states, and then multiply this by two as you at first found the area of only HALF the triangle. This should still get you to 7. Now, there are three lateral sides, not including the base, so you must multiply 7 by 3. This gets you 21.

180 square centimeters

step-by-step explanation:

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.