Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter 42cm

• • Show sub menu • Show sub menu • Show sub menu • • • • • • • • • Show sub menu • Show sub menu • • • • • • • • • • • • • Show sub menu • Show sub menu • • • • • Show sub menu • • • • • Show sub menu • • • • • Show sub menu • • • • Show sub menu • Show sub menu • • Show sub menu • • Show sub menu • Show sub menu • • • • Show sub menu • • • • Show sub menu • Show sub menu • • Show sub menu • Show sub menu • • Show sub menu • Show sub menu • Show sub menu • • • • • • be the sides of the triangle ABC. Here we have perimeter of the triangle , and . First we will find the 3rd side of the triangle by using perimeter, then we will use Heron’s formula to find the area of the given triangle. The Heron’s formula for finding the area of a triangle given by Area of a triangle = where , and are the sides of the triangle and s= semi-perimeter i.e. half of the perimeter of the triangle= . It is given that . Putting the value of and , we get 18+10+ =42 Now semi-perimeter So Therefore , area of the triangle = = = Area of triangle = . Conclusion: The area of the triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm is .

Hint: First we have to define what the terms we need to solve the problem are. Perimeter is the total length of the sides in a given two-dimensional or a three-dimensional shape. An area of a triangle is the total region that is enclosed by three sides of any triangle. Formula used: The formula for the area of the triangle is $ \sqrt $ Note: Since perimeter is given as 42cm but in the area of triangle formula we need to substitute half of the perimeter which is s and hence we divide into two and then we found the s, afterwards we applied it in the area of triangle formula.

Solve for area of the given triangle: Given, the two sides of the triangle are 18 c m and 10 c m and perimeter is 42 c m Step 1: Find the length of the third side Let us assume, a = 18, b = 10 and length of the third side be c. We know that, perimeter of triangle = a + b + c ∴ 42 = 18 + 10 + c ⇒ c = 42 - 28 = 14 Hence, the length of the third side c is 14 c m. Step 2: Find area of the triangle: By using Heron's formula, area of triangle = s ( s - a ) ( s - b ) ( s - c ), where s = a + b + c 2. Hence, s = 42 2 = 21 ∵ a + b + c = 42 c m ∴ Area of the given triangle = 21 21 - 18 21 - 10 21 - 14 = 21 × 3 × 11 × 7 ⇒Area of the given triangle = 21 11 c m 2 Hence, the area of the given triangle is 21 11 c m 2 .