Unit 1, Lesson 9
Formula for the Area of a Triangle
Grade 6
Practice
Problem 1
Select all drawings in which a corresponding height \(h\) for a given base \(b\) is correctly identified.
An image of a triangle labeled A. The top side of the triangle is labeled, b, and a dashed line labeled, h, extends straight down from the right vertex.
The triangle top side is labeled “b” and a dashed line labeled, h, extends from the center of the top side to the opposite vertex.
A triangle labeled C. The right side of the triangle is labeled, b, and a dashed line extends from the left top vertex straight down to the level of the bottom vertex labeled, h.
A triangle labeled D. The left side of the triangle is labeled, b, and a perpendicular line labeled, h, extends to the opposite vertex.
A triangle labeled E. The left side of the triangle is labeled, b, and a dashed line labeled, h, extends out from the bottom vertex at a right angle to the right side.
A triangle labeled F. The right side of the triangle is labeled, b, and a perpendicular dashed line labeled, h, extends from the side labeled, b, to the opposite vertex.
Problem 2
For each triangle, a base and its corresponding height are labeled.
3 triangles on a grid labeled A, B, C. A, base = 4, height = 6. B, base = 8, height = 4. C, base = 6, height = 4.
- Find the area of each triangle.
- How is the area related to the base and its corresponding height?
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Problem 3
Here is a right triangle. Name a corresponding height for each base.
- Side \(d\)
- Side \(e\)
- Side \(f\)
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Problem 4
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 6, 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.
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Problem 5
Andre drew a line connecting two opposite corners of a parallelogram. Select all true statements about the triangles created by the line that Andre drew.
Problem 6
Here is an octagon. (Note: The diagonal sides of the octagon are not 4 inches long.)
- While estimating the area of the octagon, Lin reasoned that it must be less than 100 square inches. Do you agree? Explain your reasoning.
- Find the exact area of the octagon. Show your reasoning.