Lesson 10

Bases and Heights of Triangles

Let’s use different base-height pairs to find the area of a triangle.

Problem 1

For each triangle, a base is labeled \(b\). Draw a line segment that shows its corresponding height. Use an index card to help you draw a straight line.

3 triangles with 1 side on each labeled b.

Problem 2

Select all triangles that have an area of 8 square units. Explain how you know.

5 triangles on grid labeled A, B, C, D, E.

Problem 3

Find the area of the triangle. Show your reasoning.

Triangle on grid, base = 6, height = 4

If you get stuck, carefully consider which side of the triangle to use as the base.

Problem 4

Can side \(d\) be the base for this triangle? If so, which length would be the corresponding height? If not, explain why not.

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.


Problem 5

Find the area of this shape. Show your reasoning.

A shape with six sides. There are two vertical sides measuring five units, two angled sides that fall 2 units over 4 units and two sides that fall 2 units over 2 units.
(From Unit 1, Lesson 3.)

Problem 6

On the grid, sketch two different parallelograms that have equal area. Label a base and height of each and explain how you know the areas are the same.

Image of a grid.
(From Unit 1, Lesson 6.)