Question 19 of 42intermediate🔧 ApplyNumerical3 marks

Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm.

Correct Answer

830\sqrt{30} cm²

Exercise: Exercise Set 6.2 | Q: 3 | (Chapter: 25)
For More Understanding

Explanation

To find the area of the triangle, we first need to determine the length of the third side using the given perimeter. Once all three sides are known, we calculate the semi-perimeter and apply Heron's formula to find the area.

Solution Steps

  1. Step 1: Find the third side of the triangle. Given perimeter = 32 cm, and two sides are 8 cm and 11 cm. Let the third side be c. 8 + 11 + c = 32 19 + c = 32 c = 32 - 19 = 13 cm.

  2. Step 2: Calculate the semi-perimeter (s). s = ½ × (Perimeter) = ½ × 32 = 16 cm.

  3. Step 3: Apply Heron's formula. Area = √[s(s - a)(s - b)(s - c)] Here, s = 16, a = 8, b = 11, c = 13. s - a = 16 - 8 = 8 s - b = 16 - 11 = 5 s - c = 16 - 13 = 3

  4. Step 4: Compute the final area. Area = √[16×816 \times 8 × 5×35 \times 3] Area = √[1920] Area = √[64×3064 \times 30] Area = 830\sqrt{30} cm²

PreviousNext