Do you remember how to calculate the area of right, acute, and obtuse triangles? Can you assign and use points on a coordinate plane? Both of these skills are imperative if you want to calculate the area of a polygon. Therefore, review these skills by working the problems in the tab set below. Use the examples presented in the first three tabs to answer the multiple choice questions in the fourth tab.
Triangle Areas
Coordinate Plane
Triangle Coordinates
Multiple Choice
Triangles can be right, acute, or obtuse. In all cases, the area is half the product of the base and the height.
Area of a Triangle
\(\large\mathsf{ A = \frac{1}{2}bh }\)
What are the base and height of each triangle? Click on each row of the next table to review this concept.
| What are the base and height of a right triangle?
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The base and height of a right triangle are the triangle sides.
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| What are the base and height of an acute triangle?
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You can choose any side to serve as the height. Then, draw a line from the opposite angle perpendicular to that side. The base is the length of that segment.
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| What are the base and height of an obtuse triangle?
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The sides connected to the obtuse angle form the base and height of an obtuse triangle. Choose one side for the base. Then, draw a line from the opposite angle perpendicular to that side. This line will always be outside the triangle.
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Do you remember how to name the points in a coordinate plane? What are the coordinates of points V, W, X, Y, and Z?
V = (0, 0)
W = (-3, -7)
X = (-7, 6)
Y = (4, 3)
Z = (9, -7)
Can you determine the area of triangles in a coordinate plane? Consider the acute and obtuse triangles in the coordinate below.
Use the next table to calculate the area of these triangles.
| Consider the obtuse triangle at the top. What is the length of the base? | 3 units |
| What is the height of the obtuse triangle? | 3 units |
| What is the area of the obtuse triangle? | \(\mathsf{ A = \frac{1}{2}bh = \frac{1}{2}(3)(3) = 4.5 \text{ square units}}\) |
| Consider the acute triangle at the bottom. What is the length of the base? | Base = 4 units |
| What is the height of the acute triangle? | Height = 2 units |
| What is the area of the acute triangle? | \(\mathsf{ A = \frac{1}{2}bh = \frac{1}{2}(4)(2) = 4 \text{ square units}}\) |
You can use a coordinate plane to calculate the area of a triangle. Use the triangles below to answer the multiple choice questions that follow.
What is the height of the acute triangle?
- 3 units
- 2 units
- 4 units
How long is the base of the acute triangle?
- 4 units
- 3 units
- 2 units
What is the area of the acute triangle?
- 16 units
- 8 units
- 12 units
What is the height of the obtuse triangle?
- 4 units
- 2 units
- 6 units
How long is the base of the obtuse triangle?
- 2 units
- 3 units
- 6 units
What is the area of the obtuse triangle?
- 12 units
- 6 units
- 3 units
Summary
Questions answered correctly:
Questions answered incorrectly:
By working these problems, you demonstrated how to calculate the area of a triangle in a coordinate plane.
