One tool used to study refraction is a glass or acrylic prism. Two of the prisms more commonly used to study light refraction are a triangular prism with an equilateral triangle for its base and a triangular prism with a right triangle for its base. In this task, you will check whether the measurements found prove the two given prisms are right prisms and whether their bases are equilateral or right triangles. The prism said to have an equilateral triangle base has the measurements shown.

Part A
Are the bases of the prism equilateral triangles? Why or why not? Note: The bases of a triangular prism are triangles.

Part B
For this prism to be a right prism, all the lateral faces must be rectangles. Is enough information given to prove the lateral faces are rectangles? Why or why not?

Part C
Without using a protractor, you can determine whether the angles are right angles by measuring the length of the diagonal and applying the converse of the Pythagorean Theorem.

The length of both diagonals for each lateral side is 13 centimeters. From this, can you prove that the lateral sides are rectangles? Why or why not?

Part D
Some of the measurements of the triangular prism with a right triangle base are shown.

What is the length of the hypotenuse of the base?

Part E
Which lateral face has the largest area, the bottom one, left one, or diagonal one? What is its area?