Find The Area Of A Scalene Triangle Math Practice Quiz

What is a scalene triangle and how to find its area?

A scalene triangle is a type of triangle that has three sides with different lengths. All three angles of a scalene triangle are also different.

To find the area of a scalene triangle, we can use a formula that involves the length of the base and the height of the triangle. The height of the triangle is the distance from the base to the top point of the triangle, called the “apex.” To find the area of a scalene triangle, we need to draw a line from the apex down to the base, creating two smaller triangles. This line is called the “altitude” of the triangle.

The formula for finding the area of a triangle is:

Area = (base * altitude) / 2

To use the formula, we need to measure the length of the base and the altitude, then plug those numbers into the formula. Let’s try an example:

Imagine we have a scalene triangle with a base of 10 inches and an altitude of 8 inches. Plugging these numbers into the formula, we get:

Area = (10 * 8) / 2 = 40 / 2 = 20 inches

So the area of this scalene triangle is 20 square inches.

It’s important to remember that the base and altitude must be in the same units, whether it’s inches, feet, or centimeters. Make sure to use the same units for both measurements when using the formula.

Sometimes, we might not know the height of a triangle, but we do know the lengths of all three sides. In this case, we can use a different formula called Heron’s formula to find the area of the triangle.

Heron’s formula is:

Area = sqrt(s * (s – a) * (s – b) * (s – c))

In this formula, “s” is a value called the “semi-perimeter” of the triangle. It’s equal to half the perimeter of the triangle, which is the total length of all three sides. “a,” “b,” and “c” are the lengths of the three sides of the triangle.

To use Heron’s formula, we need to measure the lengths of all three sides of the triangle and plug those numbers into the formula. Let’s try an example:

Imagine we have a scalene triangle with sides that are each 6 inches, 8 inches, and 10 inches long. First, we need to find the semi-perimeter of the triangle:

s = (6 + 8 + 10) / 2 = 24 / 2 = 12

Then, we can plug the values into the formula:

Area = sqrt(12 * (12 – 6) * (12 – 8) * (12 – 10))

= sqrt(12 * 6 * 4 * 2)

= sqrt(288)

= 16.97 inches

So the area of this scalene triangle is approximately 16.97 square inches.

It’s important to remember that the side lengths must be in the same units as the area, whether it’s inches, feet, or centimeters. Make sure to use the same units for all measurements when using the formula.