Fishtank Learning

6th Grade Math
Unit 7: Geometry
Lesson 2

Objective

Find the area of right triangles.

Anchor Problems - Problem 1

Explore ways to find the area of the triangle below.

Right triangle with grid lines, one side labeled as 4 units.

a. What is your best estimate for the area of this triangle? Explain how you determined your estimate.

b. What is the exact area of this triangle? Explain how you determined the exact amount.

Guiding Questions

What kind of triangle is this? How do you know?
What strategies can you think of to find an estimate of the area of the triangle?
What strategies can you think of to find an exact area of the triangle?
What relationship do you notice between the triangle and the rectangle it is inscribed in?
What information about the triangle is the same as the rectangle?
How many triangles are equal to the area of one rectangle?
How can you find the area of any triangle?

Notes

Use this Anchor Problem to guide students toward the understanding that the area of a triangle is equal to half the area of the rectangle with the same length (base) and width (height). Students may try out various strategies to find the area of the triangle, including counting the unit squares, dividing the grid into further unit squares, or recognizing the relationship between the triangle and the rectangle. Have students share their different strategies with each other either in pairs or small groups. After one student shares his or her strategy, have the other student(s) respond with their thoughts on the strategy. Do they agree? Disagree? How is the strategy similar or different from the one they used?
It may be helpful to have physical cutouts of the rectangular image above for students to physically see that the rectangle can be cut in half along the diagonal of the triangle, and then the two triangular halves match up exactly.

Anchor Problems - Problem 2

Mr. Jones told his students they each needed half a piece of paper. Calvin cut his paper horizontally and Matthew cut his paper diagonally, as shown below.

Two pieces of paper: Calvin

Which student has a half-piece of paper with the larger area? Explain your answer.

Guiding Questions

How can you find the area of Calvin’s half piece of paper?
How can you find the area of Matthew’s half piece of paper?
How do the areas compare?
What if Calvin and Matthew started out with different sized papers? Would you still get the same answer? Why or why not?

Notes

If it wasn’t introduced in Anchor Problem #1, then introduce the general formula for finding the area of a triangle and have students use it to find the area of Matthew’s half piece of paper.

Problem Set

View Problem Set

Target Task - Problem 1

A right triangle is shown below. Explain how you can find its area, and then give the value of the area in square units.

Right triangle on a grid; find area using base and height.

Target Task - Problem 2

Owen drew a straight diagonal line through a rectangle, from one corner to the other. He ended up with two right triangles, as shown below.

Rectangle divided into two congruent right triangles by a diagonal line.

Do the two triangles have the same area? Explain how you know.