All questions of Area for Class 8 Exam

Understanding the Trapezium and Rectangle
The area of a trapezium (or trapezoid) is calculated differently than that of a rectangle, primarily due to their structural characteristics.
Key Differences in Shape
- Trapezium has Two Parallel Sides:
A trapezium features one pair of parallel sides, known as the bases. This unique property distinguishes it from a rectangle, where both pairs of opposite sides are parallel.
- Rectangle has Four Right Angles:
In a rectangle, all angles are right angles (90 degrees), which allows for straightforward calculations of area using the formula: Area = Length × Width.
Area Calculation
- Area of a Trapezium:
The area of a trapezium is calculated using the formula:
Area = 1/2 × (Base1 + Base2) × Height.
This formula incorporates the lengths of both bases and the height, reflecting the trapezium's unique shape.
- Area of a Rectangle:
The area of a rectangle is simply:
Area = Length × Width.
Since rectangles have consistent lengths and widths, the calculation is more straightforward.
Conclusion
In summary, the primary difference that leads to distinct area calculations lies in the trapezium's two parallel sides, which creates a varying shape and necessitates a different formula for area. The rectangle's uniform shape, on the other hand, allows for a simpler area calculation. Understanding these differences is key to mastering geometry concepts at the Class 8 level.

Understanding the Statements
To determine which statement is always true, let's analyze each option carefully.
A) Larger perimeter means larger area
- This statement is false. Different shapes can have the same perimeter but vastly different areas. For example, a long, thin rectangle can have the same perimeter as a compact square but will have a smaller area.
B) Same perimeter means same area
- This statement is also false. Different shapes can have the same perimeter but different areas. For instance, two different rectangles with the same perimeter can have varying lengths and widths, leading to differing areas.
C) Same base and height means same area (for triangles)
- This statement is true. For triangles, if the base and height are identical, the area will always be the same, regardless of the triangle's shape. The area of a triangle is calculated using the formula (1/2) * base * height.
D) Area depends only on perimeter
- This statement is false. Area is influenced by the dimensions of a shape and not solely by its perimeter. Two shapes can have the same perimeter but different areas, as previously mentioned.
Conclusion
Among the options provided, the correct and always true statement is:
- C) Same base and height means same area (for triangles)
This statement accurately reflects the fundamental property of triangles, ensuring consistency in area calculations based on these dimensions.