Lesson 8: Practice Problems

Problem 1

Select all drawings in which a corresponding height for a given base is correctly identified.

  1. triangle, the top side is labeled “b” and a dashed line extending straight down from the right vertex is labeled “h”.
  2. triangle, the top side is labeled “b” and a dashed line extends from the center of the top side to the opposite vertex labeled “h”.
  3. triangle, the right side is labeled “b” and a dashed line extends from the right top vertex straight down to the level of the bottom vertex.
  4. triangle, the left side is labeled “b” and a perpendicular line labeled “h” extends to the opposite vertex.
  5. triangle, the right side is labeled “b” and a dashed line labeled “h” extends out from the bottom vertex at a right angle to the left side.
  6. triangle, the right side is labeled “b” and a perpendicular dashed line labeled “h” extends from the side labeled “b” and extends to the opposite vertex.

Problem 2

For each triangle, a base and its corresponding height are labeled.

  1. 3 blue triangles on a blank grid with their base and height labeled.

    Find the area of each triangle.

  2. How is the area related to the base and its corresponding height?

Problem 3

Here is a right triangle. Name a corresponding height for each base.

A triangle with sides labeled d, e, and f. The angle opposite side D is a right angle. A segment labeled g is perpendicular to side d and extends to the opposite vertex.

  1. Side

  2. Side

  3. Side

Problem 4 From Unit 1 Lesson 7

Find the area of the shaded triangle. Show your reasoning.

A square with a shaded triangle contained inside it. The left and bottom sides of the square are labeled six, and the right side is labeled 2 above the point where vertex of the shaded triangle meets the side, and 4 below the point where the vertex meets the side.

Problem 5 From Unit 1 Lesson 6

Andre drew a line connecting two opposite corners of a parallelogram. Select all true statements about the triangles created by the line Andre drew.

A parallelogram with a line connecting two opposite corners. The parallelogram has a base of 3 units and a height of 9 units.

  1. Each triangle has two sides that are 3 units long.

  2. Each triangle has a side that is the same length as the diagonal line.

  3. Each triangle has one side that is 3 units long.

  4. When one triangle is placed on top of the other and their sides are aligned, we will see that one triangle is larger than the other.

  5. The two triangles have the same area as each other.

Problem 6 From Unit 1 Lesson 3

Here is an octagon.

An octagon with straight sides that are 4 inches long, and angled sides that are both 3 inches high and 3 inches wide.

  1. While estimating the area of the octagon, Lin reasoned that it must be less than 100 square inches. Do you agree? Explain your reasoning.

  2. Find the exact area of the octagon. Show your reasoning.