Heron's Formula : In some cases, length of each side of the triangle are given but height of the triangle is neither given nor we are able to find in any way, then to find the area of such type of triangle, we use Heron's formula which is given below.
Area of triangle = , where a,b,c are length of the sides of a triangle and s is the semi-perimeter of the triangle i.e.
Example: Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm. Solution : We divide the quadrilateral ABCD in two triangle ABC and ACD For ABC, a = 3, b = 4, c = 5 and Area (ABC) = = = 6 Similarly, for ACD, a = 5 cm, b = 5 cm, c = 4 cm and s = Area ( ACD ) = = = = Area of quadrilateral ABCD = Area of triangle ABC+ Area of triangle ACD = + |
The perimeter of a triangular field is 144 m and the ratio of sides 3 :4: 5, the area of the field is | |||
Right Option : A | |||
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The sides of triangle are 11 m 60 m and 61 m. The altitude to the smallest side is | |||
Right Option : D | |||
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The area of a triangle with each side equals 5.1 meters and third side 4.6 meters is _______________________. | |||
Right Option : A | |||
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