Altitude of a Triangle

Grade 6 Math Worksheets

The perpendicular line segment traced from the triangle’s vertex to its opposite side is its altitude. Depending on the kind of triangle, it could lie inside or outside of the triangle.

When measuring a triangle’s area in relation to its base, the altitude of the triangle essentially indicates its height.

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Altitude of a Triangle - Grade 6 Math Worksheet PDF

This is a free printable / downloadable PDF worksheet with practice problems and answers. You can also work on it online.

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Formula for Altitude

The following table summarizes the key formulas for a triangle’s altitude. These formulas are explained in depth in the section that follows.

Altitude of an Equilateral Triangle

The altitude of an equilateral triangle can be determined using the formula given below:

Altitude of a Scalene Triangle

The altitude of a scalene triangle can be determined using the formula given below:

Altitude of an Isosceles Triangle

The altitude of an isosceles triangle can be determined using the formula given below:

https://mathmonks.com/wp-content/uploads/2021/05/Altitude-of-Isosceles-Triangle-Formula.jpg

Altitude of a Right Triangle

The altitude of a right triangle can be determined using the formula given below:

https://mathmonks.com/wp-content/uploads/2021/05/Altitude-of-a-Right-Triangle-Formula.jpg

Altitude of an Obtuse Triangle

In an obtuse triangle, the altitude lies outside the triangle. The base is extended and the altitude is drawn from the opposite vertex to its base. The altitude of an obtuse triangle can be determined using the formula given below:

https://mathmonks.com/wp-content/uploads/2021/05/Altitude-of-Obtuse-Triangle-Formula.jpg

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Solved Sample Examples

1. Find the altitude of an equilateral triangle with sides measuring 6 cm.

Solution:

As we know,
h = √3/2a, here a = 6 cm
= √3/2 x 6
= 3√3 [∵√3 ~ 1.732]
= 5.196

Calculate the altitude of a scalene triangle having sides 5 cm, 6 cm, and 7 cm.

Solution:

As we know,
h = 2√s(s–a)(s–b)(s–c)/b, here a = 5 cm, b = 6 cm, and c = 7 cm
In the given triangle,
s = (5+6+7)/2 = 9 cm
Thus,
h = 2√9(9-5)(9-6)(9-7)/6
= 2√216/6
= 2√36
=2√6 x 6
= 12 cm

Find the altitude of an isosceles triangle with sides measuring 6 cm, 4 cm and 6 cm.

Solution:

As we know,
h = √a2 – b2/4, here a = 6 cm, b = 4 cm
= √62 – ¼(4)2
= √32 cm

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FAQs

What is the altitude of a triangle?

The altitude of a triangle is a perpendicular line segment drawn from a vertex to the line containing the opposite side.

How is the altitude different from the base of a triangle?

The base of a triangle is one of its sides, while the altitude is a perpendicular line segment from a vertex to the opposite side.

Is the altitude always inside the triangle?

No, the altitude can be inside, outside, or coincident with the sides of the triangle, depending on its construction.

Can a triangle have more than one altitude?

Yes, a triangle can have three altitudes, each drawn from a different vertex to the line containing the opposite side.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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