Areas of Triangles

In this lesson, we will look at three different formulas that can be used to calculate the areas of triangles.

Formula 1:

If we are given the base of the triangle and the perpendicular height then we can use the formula.

Area =

The height of a triangle is the perpendicular distance from a vertex to the base of the triangle.

Any of the 3 sides of a triangle can be used as a base. It all depends on where the height is drawn.

The following video shows an example of using the above formula to calculate the area of a triangle.

The following video shows how we can use the Pythagorean theorem to get the height of an isosceles triangle and then calculate the area of the triangle.

Formula 2:

If we are given three sides of a triangle, we can use Heron’s formula:

Formula 3:

If we are given the lengths of two sides of a triangle and the size of angle between them we can use the formula:

Area of triangle = ab sin C

By considering sin A and sin B in a similar way, we obtain

Area = bc sin A = ac sin B

Remember that the given angle must be between the two given sides.

Example:

Find the area of triangle PQR if p = 6.5 cm, r = 4.3 cm and Ð Q = 39˚. Give your answer correct to 2 decimal places.

Solution:

Area of triangle PQR

= pr sin Q

= sin 39˚

= 8.79 cm²

The following video shows how to use the abouve formula to find the area of an oblique triangle.

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