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How do engineers calculate the exact sheet metal needed to build an oil tank or paint a bridge? Mensuration calculates the surface area and volume of ...
How do engineers calculate the exact sheet metal needed to build an oil tank or paint a bridge? Mensuration calculates the surface area and volume of two-dimensional and three-dimensional geometric figures.
Why This Chapter Matters
In Class 8 Mathematics, "Area" delivers rigorous mathematical reasoning, algebraic precision, and geometric mastery aligned with the 2026–27 NCERT curriculum.
Before You Begin (Prerequisites)
- Area of rectangle ($l \times b$) and triangle ($\frac{1}{2}bh$).
- Perimeter calculations.
- Square and cubic units.
What You Will Learn (Core Objectives)
- Calculate areas of Trapezius and general quadrilaterals by triangulating.
- Calculate areas of Rhombuses using diagonals ($\frac{1}{2} d_1 d_2$).
- Calculate Total Surface Area (TSA) and Lateral Surface Area (LSA) of Cubes, Cuboids, and Cylinders.
- Calculate Volumes of Cubes ($s^3$), Cuboids ($lbh$), and Cylinders ($\pi r^2 h$).
- Distinguish between Volume (space occupied) and Capacity (liquid volume in liters).
Chapter Roadmap & Progression
1
1. Area of Trapezium and General Qu...
2
2. Surface Area of 3D Solids
3
3. Volume and Capacity
Complete Concept Guide (100% Curriculum Coverage)
1. Area of Trapezium and General Quadrilaterals
- Area of Trapezium: Half the sum of parallel sides times perpendicular distance: $$\mathbf{\text{Area} = \frac{1}{2}(a + b) \times h}$$
- Area of Rhombus: Half the product of its diagonals: $$\mathbf{\text{Area} = \frac{1}{2} \times d_1 \times d_2}$$
- General Quadrilateral: Split along a diagonal $d$ with perpendicular offsets $h_1, h_2$: $\text{Area} = \frac{1}{2}d(h_1 + h_2)$.
2. Surface Area of 3D Solids
- Cuboid: $\text{TSA} = 2(lb + bh + hl)$; $\text{LSA} = 2h(l + b)$ (Area of 4 walls).
- Cube: $\text{TSA} = 6s^2$; $\text{LSA} = 4s^2$.
- Cylinder: $\text{Curved Surface Area (CSA)} = 2\pi rh$; $\text{TSA} = 2\pi r(r + h)$.
3. Volume and Capacity
Volume is the 3D space occupied: $\text{Cuboid} = lbh$; $\text{Cube} = s^3$; $\text{Cylinder} = \pi r^2 h$.
Capacity conversion: $1\text{ m}^3 = 1000\text{ Liters}$, and $1000\text{ cm}^3 = 1\text{ Liter}$.
Visual Learning & Conceptual Map
Area Mathematical Matrix
Core formulas, geometric proofs, and computational algorithms
Mathematical Framework
1. Area of Trapezium and General Quadrilaterals • 2. Surface Area of 3D Solids • 3. Volume and Capacity
Chapter Summary & 10 Key Takeaways
Takeaway 1
Trapezium Area: $\frac{1}{2}(a + b)h$.
Takeaway 2
Rhombus Area: $\frac{1}{2} d_1 d_2$.
Takeaway 3
Cuboid Volume: $l \times b \times h$; Cylinder Volume: $\pi r^2 h$.
Takeaway 4
Cylinder CSA: $2\pi rh$; TSA: $2\pi r(r + h)$.
Takeaway 5
Capacity: $1\text{ m}^3 = 1,000\text{ Liters}$.
Check Your Understanding (Diagnostic Practice Questions)
Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.
1
Find the area of a trapezium whose parallel sides are 10 cm and 12 cm and height is 4 cm.
Reveal Answer & Explanation
Answer: $\text{Area} = \frac{1}{2}(10 + 12) \times 4 = \frac{1}{2}(22) \times 4 = 44\text{ cm}^2$.
Area = 1/2(a+b)h.
2
The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
Reveal Answer & Explanation
Answer: $\text{Area} = \frac{1}{2} \times 7.5 \times 12 = 7.5 \times 6 = 45\text{ cm}^2$.
Area = 1/2 * d1 * d2.
3
Find the volume of a cylinder whose base radius is 7 cm and height is 10 cm.
Reveal Answer & Explanation
Answer: $\text{Volume} = \pi r^2 h = \frac{22}{7} \times 7 \times 7 \times 10 = 22 \times 70 = 1,540\text{ cm}^3$.
Volume = pi * r^2 * h.
4
How many liters of water can a cuboidal water tank of dimensions $2\text{ m} \times 1.5\text{ m} \times 1\text{ m}$ hold?
Reveal Answer & Explanation
Answer: $\text{Volume} = 2 \times 1.5 \times 1 = 3\text{ m}^3$. Since $1\text{ m}^3 = 1000\text{ L}$, capacity is $3,000\text{ Liters}$.
1 m^3 = 1000 Liters.
5
Find the total surface area of a cube of side 5 cm.
Reveal Answer & Explanation
Answer: $\text{TSA} = 6s^2 = 6 \times 5^2 = 6 \times 25 = 150\text{ cm}^2$.
TSA = 6 * side^2.
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Timed CBT Practice Tests (Exam Simulator)
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