Find the area of a triangle two sides of which are 8 cm and 11 cm and the perimeter is 32 cm

Hint: In this question, we first need to write the relation between the sides of the triangle and the perimeter given by the formula \[P=a+b+c\]. Now, on further substituting the value of perimeter and the two sides we get the third side of the triangle. Then find the area of the triangle by using the formula \[Area=\sqrt\]. Note: Instead of using Heron's formula to find the area of the triangle we can also find it by multiplying the base and height and then divide by 2 which gives the area. Both methods give the same result but finding the height will be lengthy so it is better to use Heron's formula.It is important to note that while substituting the values and simplifying we need to substitute the appropriate values because there is a chance for calculation mistake which changes the final result.

Let s be the semi-perimeter and a, b and c are sides of a triangle Using Heron's formula, Area of triangle = √s(s – a)(s – b)(s – c) a = 8 cm, b = 11 cm c = 32 - (8 + 11) = 13 cm s = (8 + 11 + 13)/2 = 16 Area of triangle = √16(16 – 8)(16 – 11)(16 – 13) ⇒ Area of triangle = √16 × 8 × 5 × 3 ⇒√2 × 2 × 2 × 2 × 2 × 2 ×2 × 5 × 3 ⇒ 2 × 2 × 2 ×√30 = 8√30 cm 2

Find the area of a triangle, two sides of which are $$ Answer and Explanation: 1

Hint: Here in the above question we need to find area of the triangle As we know that perimeter is sum of the length of the sides of triangles and in this question perimeter and the length of the two sides of triangle is given so firstly we will find the third side of the triangle by using the perimeter of triangle. Later on we will use these three sides in Heron’s formula to find the area of the triangle. Formula used: The formula used in the above question for finding the area of triangle is Heron’s Formula which is \[A = \sqrt \] ”. Note: Remember while using Heron’s formula for finding the area of the triangle length all the three sides of the triangle is required and this is a major challenge. So for the above question we need to find the third side of the triangle also for finding the area of the triangle. Here we used Heron’s formula as length can be easily calculated with the help of perimeter and area of triangles can be calculated easily by this formula without the measurement of angles of triangle.