CBSE style practice questions for Heron’s Formula based on past exam patterns
### **📌 Section A: Basic Questions (1-2 Marks Each)**
1️⃣ Find the area of a triangle whose sides are **9 cm, 12 cm, and 15 cm** using Heron’s formula.
2️⃣ A triangle has sides **5 cm, 12 cm, and 13 cm**. Calculate its area.
3️⃣ Find the semi-perimeter of a triangle with sides **18 cm, 24 cm, and 30 cm**.
4️⃣ A triangle has a perimeter of **40 cm**. Two of its sides are **15 cm and 12 cm**. Find the third side if the area is **80 cm²**.
5️⃣ If the sides of a triangle are in the ratio **3:4:5** and its perimeter is **36 cm**, find its area.
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### **📌 Section B: Intermediate-Level Questions (3-4 Marks Each)**
6️⃣ A triangular park has sides **40 m, 50 m, and 60 m**. Find the area of the park and the cost of laying grass at ₹5 per square meter.
7️⃣ Find the height of a triangle with **base = 14 cm** and **area = 84 cm²** using Heron’s formula.
8️⃣ A triangle has sides **7 cm, 8 cm, and 9 cm**. Find the **difference** between its area using Heron’s formula and using the base-height formula.
9️⃣ Find the area of a **right-angled triangle** whose hypotenuse is **13 cm** and one of the sides is **5 cm**, using Heron’s formula.
🔟 A farmer has a **triangular field** with sides **26 m, 28 m, and 30 m**. He wants to fence it with three rounds of wire. If the cost of fencing is ₹15 per meter, find the total fencing cost.
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### **📌 Section C: Higher Order Thinking (HOTs) Questions (5-6 Marks Each)**
1️⃣1️⃣ A **quadrilateral** is divided into **two triangles** with sides **6 cm, 8 cm, 10 cm** and **5 cm, 12 cm, 13 cm**. Find its total area using Heron’s formula.
1️⃣2️⃣ The sides of a triangular garden are **80 m, 90 m, and 100 m**. Find the cost of **paving** the garden with tiles at ₹20 per square meter.
1️⃣3️⃣ A **trapezium** is divided into two triangles of sides **10 cm, 12 cm, 14 cm** and **8 cm, 15 cm, 17 cm**. Find the total area of the trapezium.
1️⃣4️⃣ Find the area of an **isosceles triangle** with base **24 cm** and equal sides **26 cm** using Heron’s formula.
1️⃣5️⃣ A **triangle-shaped flag** has sides **20 cm, 21 cm, and 29 cm**. Find the **cost of coloring** it at ₹8 per cm².
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### **📌 Bonus Challenge Questions**
🎯 A **triangular swimming pool** has sides **50 m, 80 m, and 100 m**. The **depth is 2.5 m**. Find the **total water capacity** in liters. (1 m³ = 1000 liters)
🎯 A **triangular plot** has sides **25 m, 39 m, and 50 m**. The government wants to **build a circular park inside** that covers the maximum possible area. Find the **radius of the largest inscribed circle** in the triangle.
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