Find the area of a triangular park ABC with sides 50m, 80m, and 120m using Heron's formula.

Step 1: Calculate the semi-perimeter

Heron's formula requires the semi-perimeter, denoted by $s$. This is half the sum of the lengths of the three sides of the triangle. Given the side lengths $a = 50\text{ m}$, $b = 80\text{ m}$, and $c = 120\text{ m}$, we sum them up and divide by 2.

Step 2: Substitute values into semi-perimeter formula

Substituting the given side lengths into the formula, we get $s = \frac{50 + 80 + 120}{2} = \frac{250}{2} = 125\text{ m}$.

Step 3: Apply Heron's formula

Heron's formula provides a way to calculate the area of a triangle when only the lengths of its three sides are known. The formula is $\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter and $a, b, c$ are the side lengths.

Step 4: Substitute values into Heron's formula

Now we substitute the calculated semi-perimeter $s = 125\text{ m}$ and the given side lengths $a = 50\text{ m}$, $b = 80\text{ m}$, $c = 120\text{ m}$ into Heron's formula.

Step 5: Calculate the area

Performing the subtractions inside the parentheses and then multiplying the terms, we get $\text{Area} = \sqrt{125 \times 75 \times 45 \times 5} = \sqrt{2109375}$. Finally, we calculate the square root to find the area, which is approximately $1452.36\text{ m}^2$.

More from this chapter

• **Fig. 13.36** shows a circle with center O. A line segment BC passes through O as a diameter. A chord AB is drawn, and a vertical segment AC connects A to C. A
• एक पार्क में बने 5 m त्रिज्या वाले वृत्त पर खड़ी तीन लड़कियाँ रेशमा, सलमा एवं मनदीप खेल रही हैं। रेशमा एक गेंद को सलमा के पास, सलमा मनदीप के पास तथा मनदीप रेशमा
• The side of a triangular plot are in the ratio 3:5:7,it's perimeter is 300 m. Find its area
• 23. The perimeter of an isosceles triangle is 32 cm. If each equal side is (5)/(6)th of the base, find the area of the triangle. (CBSE-2025) 24. Express the equ
• Find the area of a triangle whose sides are 13 cm, 14 cm and 15 cm, using Heron's formula.
• Construct a triangle ABC with AB = 5 cm, BC = 6 cm and angle B = 60 degrees and find its area.
• Find the volume of a right circular cone with base radius 6 cm and height 7 cm. Use pi = 22/7.

All Measuring Space: Perimeter and Area solutions →