# Area of a Triangle - Mathematics Form 2 Notes

## Area of a Triangle Given Two Sides and an Included Angle

The area of a triangle is given by A = 1/2bh but sometimes we use other formulas too as follows.

If the length of two sides and an included angle of a triangle are given, the area of the triangle is given by A = 1/2 absinθ

Example

In the figure above PQ is 5 cm and PR is 7 cm angle QPR is 500. Find the area of the the triangle.

Solution

Using the formulae by A = 1/2absinθ a= 5 cm b = 7 cm and θ = 500
Area = 1/2 x 5 x 7 sin 500
=2.5 x 7 x 0.7660
=13.40
cm2

## Area of the Triangle, Given the Three Sides.

Example

Find the area of a triangle ABC in which AB = 5 cm, BC = 6 cm and AC =7 cm.

Solution

When only three sides are given us the formulae

A = √[s(s−a)(s−b)(s−c)] Hero’s formulae
S
= 1/2 of the perimeter of the triangle
= 1/2(a + b + c) a, b, c are the lengths of the sides of the triangle.

= 1/2(6+7+5= 9 And A =√[9(9−6)(9−7)(9−5)]
=√(9 x 3 x 2 x 4)
= √216
= 14.70 cm
2

## Past KCSE Questions on the Topic.

1. The sides of a triangle are in the ratio 3:5:6. If its perimeter is 56 cm, use the Heroes formula to find its area (4mks)
2. The figure below is a triangle XYZ. ZY = 13.4cm, XY = 5cm and angle xyz = 57.7o

1. Calculate
1. Length XZ. (3mks)
2. Angle XZY. (2 mks)
2. If a perpendicular is dropped from point X to cut ZY at M, Find the ratio MY:ZM.(3 mks)
3. Find the area of triangle XYZ. (2 mks)

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