Area and Perimeter of
Triangles
Bill Zahner
Lori Jordan
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Printed: March 6, 2016
AUTHORS
Bill Zahner
Lori Jordan
www.ck12.org
C HAPTER
Chapter 1. Area and Perimeter of Triangles
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Area and Perimeter of
Triangles
Here you’ll learn how to calculate the area and perimeter of a triangle and how the area of triangles relates to the
area of parallelograms.
What if you wanted to find the area of a triangle? How does this relate to the area of a parallelogram? After
completing this Concept, you’ll be able to answer questions like these.
Watch This
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/137560
CK-12 Foundation: Chapter10AreaandPerimeterofTrianglesA
Learn more about the area of triangles by watching the video at this link.
Guidance
If we take parallelogram and cut it in half, along a diagonal, we would have two congruent triangles. Therefore, the
formula for the area of a triangle is the same as the formula for area of a parallelogram, but cut in half.
The area of a triangle is A = 12 bh or A = bh
2 . In the case that the triangle is a right triangle, then the height and base
would be the legs of the right triangle. If the triangle is an obtuse triangle, the altitude, or height, could be outside of
the triangle.
Example A
Find the area of the triangle.
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This is an obtuse triangle. To find the area, we need to find the height of the triangle. We are given the two sides of
the small right triangle, where the hypotenuse is also the short side of the obtuse triangle. From these values, we see
that the height is 4 because this is a 3-4-5 right triangle. The area is A = 12 (4)(7) = 14 units2 .
Example B
Find the perimeter of the triangle from Example A.
To find the perimeter, we would need to find the longest side of the obtuse triangle. If we used the dotted lines in the
picture, we would see that the longest side is also the hypotenuse of the right triangle with legs 4 and 10. Use the
Pythagorean Theorem.
42 + 102 = c2
16 + 100 = c2
√
c = 116 ≈ 10.77
The perimeter is 7 + 5 + 10.77 = 22.77 units
Example C
Find the area of a triangle with base of length 28 cm and height of 15 cm.
The area is 21 (28)(15) = 210 cm2 .
Watch this video for help with the Examples above.
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/137561
CK-12 Foundation: Chapter10AreaandPerimeterofTrianglesB
Guided Practice
Use the triangle to answer the following questions.
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Chapter 1. Area and Perimeter of Triangles
1. Find the height of the triangle.
2. Find the perimeter.
3. Find the area.
Answers:
1. Use the Pythagorean Theorem to find the height.
82 + h2 = 172
h2 = 225
h = 15 in
2. We need to find the hypotenuse. Use the Pythagorean Theorem again.
(8 + 24)2 + 152 = h2
h2 = 1249
h ≈ 35.3 in
The perimeter is 24 + 35.3 + 17 ≈ 76.3 in.
3. The area is 12 (24)(15) = 180 in2 .
Interactive Practice
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/113014
Explore More
Use the triangle to answer the following questions.
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1. Find the height of the triangle by using the geometric mean.
2. Find the perimeter.
3. Find the area.
Find the area of the following shape.
4.
5. What is the height of a triangle with area 144 m2 and a base of 24 m?
For problems 6 and 7 find the height and area of the equilateral triangle with the given perimeter.
6. Perimeter 18 units.
7. Perimeter 30 units.
8. Generalize your results from problems 6 and 7 into a formula to find the height and area of an equilateral
triangle with side length x.
Find the area of each triangle.
9.
10.
11.
12.
13.
14.
15.
Find the area of a triangle with a base of 10 in and a height of 12 in.
Find the area of a triangle with a base of 5√in and a height of 3 in.
An equilateral triangle with a height of 6 3√units.
A 45-45-90 triangle with a hypotenuse of 5 2 units.
A 45-45-90 triangle with a leg of 12 units.
A 30-60-90 triangle with a hypotenuse of 24 units.
A 30-60-90 triangle with a short leg of 5 units.
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 10.3.
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