The Area of a Triangle

The area of a triangle is always  half the product of the height and base.

A=½ (base × height)

Any side can be a base, but every base has only one height. The height is the line from the opposite vertex and perpendicular to the base. In the picture above, the base CB has one and only one height. The illustration below shows how any leg of the triangle can be a base and the height always extends from the vertex of the opposite side and is perpendicular to the base.

The picture below shows you that the height can actually extend outside of the triangle. So technically the height does not necessarily intersect with the base.

Explanation of the Area of a Triangle

Example 1

To find the area of the triangle on the left, use the formula above.

A= (b*h)/2
A=(10*3)/2 = 30/2 = 15

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Problem 1
What is the area of the triangle in the following picture?

Answer To find the area of the triangle on the left, substitute the base and the height into the formula for area. Area = ½(base)(height) Area = ½(3)(3) Area = 4.5 inches squared

Problem 2
Calculate the area of the triangle pictured below.

Answer To find the area of the triangle on the left, substitute the base and the height into the formula for area. Area = ½(base)(height) Area = ½(24)(27.6) Area = 331.2 inches squared

Problem 3
Calculate the area of the triangle pictured below.

Answer To find the area of the triangle on the left, substitute the base and the height into the formula for area. Area = ½(base)(height) Area = ½(12)(2.5) Area = 15 inches squared (Rounded to the nearest tenth)

Problem 4
Calculate the area of the triangle pictured below.

Answer To find the area of the triangle on the left, substitute the base and the height into the formula for area. Area = ½(base)(height) Area = ½(12)(3.9) Area = 23.4 inches squared (Rounded to the nearest tenth)

Problem 5
Calculate the area of the triangle pictured below.

Answer To find the area of the triangle on the left, substitute the base and the height into the formula for area. Area = ½(base)(height) Area = ½(14)(4) Area = 23.4 inches squared (Rounded to the nearest tenth)

Problem 6
What is the area of the following triangle?

Answer This problems involves 1 small twist. You must decide which of the 3 bases to use. Just remember that base and height are perpendicular. Therefore, the base is '11' since it is perpendicular to the height of 13.4 To find the area of the triangle on the left, substitute the base and the height into the formula for area. Area = ½(base)(height) Area = ½(11)(13.4) Area = 73.7 inches squared (Rounded to the nearest tenth)

Problem 7
What is the area of the following triangle?

Answer This problems involves 1 small twist. You must decide which of the 3 bases to use. Just remember that base and height are perpendicular. Therefore, the base is '12' since it is perpendicular to the height of 5.9 To find the area of the triangle on the left, substitute the base and the height into the formula for area. Area = ½(base)(height) Area = ½(12)(5.9) Area = 35.4 inches squared (Rounded to the nearest tenth)

Problem 8
What is the area of the following triangle?

Answer Like the last problem, you must decide which of the 3 bases to use. Just remember that base and height are perpendicular. Therefore, the base is '4' since it is perpendicular to the height of 17.7 To find the area of the triangle on the left, substitute the base and the height into the formula for area. Area = ½(base)(height) Area = ½(4)(17.7) Area = 35.4 inches squared (Rounded to the nearest tenth)

Problem 8
What is the area of the following triangle?

Answer Again, you must decide which of the 3 bases to use. Just remember that base and height are perpendicular. Therefore, the base is '22' since it is perpendicular to the height of 26.8 To find the area of the triangle on the left, substitute the base and the height into the formula for area. Area = ½(base)(height) Area = ½(22)(26.8) Area = 294.8 inches squared (Rounded to the nearest tenth)

If you are interested in practicing finding the height of a triangle, given its area, visit this link