Question

A triangle has sides of length 7 cm, 5 cm and 8 cm.What is area of triangle ? Do it fast plz using herons formula

Answer 1

The answer is 17.32 cm².

Given: Side 1 of the triangle (a) = 7 cm

           Side 2 of the triangle (b) = 5 cm

            Side 3 of the triangle (c) = 8 cm

To find: the area of the triangle using Heron's formula

Solution:

Perimeter of the triangle = Side 1 + Side 2 + Side 3

                                        = (7 + 5 + 8) cm

                                        = 20 cm

∴ Semi-perimeter (s) = $\frac{Perimeter}{2}$

                                  = $\frac{20}{2}$ cm

                                  = 10 cm

Using Heron's formula,

∴ Area of the triangle = $\sqrt{s (s - a) (s-b)(s-c)}$

                                 = $\sqrt{10 (10-7)( 10-5)(10-8)}$

                                 = $\sqrt{10 \times 3 \times 5 \times 2 }$

                                 = $\sqrt{300}$

                                 = 17.32 cm²

Answer) The area of the triangle is 17.32 cm².

Area

• Area refers to the space which is occupied by a flat or three-dimensional object.

• Perimeter refers to the boundary line of the plane object. It only measures the outer line of the shape.

• In Heron's formula, we need to find the perimeter of the triangle. Then we need to find the semi-perimeter by dividing the perimeter by 2.

• This semi-perimeter is used to calculate the area of the triangle. It is multiplied by the subtractions of other sides of the triangle. Then the square root of that answer is taken as the area of a triangle.

• A right-angled triangle is calculated differently. It has a separate formula.

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