Mathematics
Grade 7
15 min
Area of triangles
Area of triangles
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1
Introduction & Learning Objectives
Learning Objectives
Identify the base and corresponding perpendicular height of any triangle.
Recall and accurately apply the formula for the area of a triangle.
Calculate the area of various types of triangles (acute, obtuse, right) given their base and height.
Solve real-world problems involving the area of triangles.
Determine a missing base or height when the area and the other dimension are provided.
Understand and correctly use appropriate square units for area measurements.
Ever wondered how much fabric you'd need to make a triangular flag, or how much paint to cover a triangular wall? 📐 Let's find out how to measure these spaces!
In this lesson, you'll learn the essential formula and techniques to calculate the area of any triangle. Understanding thi...
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Key Concepts & Vocabulary
TermDefinitionExample
TriangleA polygon with three straight sides and three angles.An equilateral triangle, an isosceles triangle, or a right triangle are all examples of triangles.
Base (of a triangle)Any side of a triangle chosen to be the bottom. You can choose any of the three sides as the base.If a triangle has sides of 5 cm, 7 cm, and 8 cm, you could choose the 8 cm side as the base.
Height (Altitude)The perpendicular distance from the chosen base to the opposite vertex. It forms a right angle (90°) with the base.For a triangle with a base of 10 cm, if the distance from the opposite corner straight down to the base is 6 cm, then 6 cm is the height.
PerpendicularLines, segments, or rays that intersect to form a right angle (90 degrees).The height of a triangle is always perpendicular...
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Core Formulas
Area of a Triangle Formula
`A = \frac{1}{2}bh`
To find the area (A) of any triangle, multiply one-half by the length of its base (b) and its corresponding height (h). Remember, the height must be perpendicular to the chosen base.
Finding a Missing Dimension (Base or Height)
`b = \frac{2A}{h}` or `h = \frac{2A}{b}`
If you know the area (A) and either the base (b) or the height (h), you can rearrange the area formula to find the missing dimension. Double the area and then divide by the known dimension.
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Challenging
A rectangular piece of paper is 10 inches wide and 16 inches long. A triangle is cut from it. The triangle's base is the same as the paper's width, and its height is the same as the paper's length. What is the area of the paper LEFT OVER after the triangle is cut out?
A.160 in²
B.80 in²
C.40 in²
D.120 in²
Challenging
If a triangle's base is doubled and its height is tripled, how many times larger is the new triangle's area compared to the original area?
A.2 times larger
B.3 times larger
C.6 times larger
D.5 times larger
Challenging
An isosceles triangle has a base of 12 cm and two equal sides of 10 cm. The height to the base is 8 cm. What is the area of the triangle?
A.48 cm²
B.60 cm²
C.40 cm²
D.120 cm²
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