Lesson 11: Practice Problems

Problem 1

Here are two three-dimensional figures.

Two figure labeled A and B. A is a triangular prism with rectangular sides. B is a triangular prism with triangle sides.

Tell whether each of the following statements describes Figure A, Figure B, both, or neither.

  1. This figure is a polyhedron.

  2. This figure has triangular faces.

  3. There are more vertices than edges in this figure.

  4. This figure has rectangular faces.

  5. This figure is a pyramid.

  6. There is exactly one face that can be the base for this figure.

  7. The base of this figure is a triangle.

  8. This figure has two identical and parallel faces that can be the base.

Problem 2

A cylinder with bases in the shape of octagons.

  1. Is this polyhedron a prism, a pyramid, or neither? Explain how you know.

  2. How many faces, edges, and vertices does it have?

Problem 3

A arrow shape made up of 2 triangles the same size attached on either side of a rectangle which is attached to two other rectangles of differing sizes.

  1. What polyhedron can be assembled from this net? Explain how you know.

  2. Find the surface area of this polyhedron. Show your reasoning.

Problem 4 From Unit 1 Lesson 8

  1. A parallelogram has a base of 12 meters and a height of 1.5 meters. What is its area?

  2. A triangle has a base of 16 inches and a height of inches. What is its area?

  3. A parallelogram has an area of 28 square feet and a height of 4 feet. What is its base?

  4. A triangle has an area of 32 square millimeters and a base of 8 millimeters. What is its height?

Problem 5 From Unit 1 Lesson 3

Find the area of the shaded region. Show or explain your reasoning.

A blue triangle with a height line of 3 in the middle hitting a white square cutout with sides of 2. On either side of the square, there are triangle bases of 6.