Moderate Level Worksheet

Part A: Subjective Questions - Very Short Answer (1 Mark Each)

In this moderate level, we'll explore more complex calculations, parallelograms, and problem-solving.

Let's deepen our understanding of area and perimeter!

1. Write the formula for the area of a triangle.

Area = one halftwo × baseside × heightlength

Or: Area = (1/2) × b × h

Perfect! Triangle area uses base and perpendicular height.

2. Find the perimeter of a rectangle of sides 8 m and 5 m.

Perimeter = 2(l + b) = 2( + )

= 2 × = m

Excellent! Perimeter = 26 m.

3. Find the area of a square whose perimeter is 24 cm.

Perimeter = 4 × side =

Side = 24 ÷ = cm

Area = × = cm²

Perfect! Side = 6 cm, Area = 36 cm².

4. Define perimeter and give one example.

Perimeter is the total lengtharea of the boundarysurface

Example: Perimeter of square with side 5 cm = cm

Great! Perimeter measures the boundary length.

5. Find the area of a rectangle with length 15 m and breadth 8 m.

Area = l × b = ×

= m²

Correct! Area = 120 m².

6. Write the relation between area and perimeter of a square.

If perimeter = P, then side = P ÷

Area = (P ÷ 4) squaredtimes 2

Excellent! Area = (Perimeter/4)².

7. Find the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm.

Perimeter = + +

= cm

Perfect! Perimeter = 24 cm.

8. Write the area of a parallelogram.

Area = baseside × heightwidth

Correct! Parallelogram area = base × perpendicular height.

9. Write one difference between area and perimeter.

Area: Measures surfaceboundary, unit is square unitslinear units

Perimeter: Measures boundarysurface, unit is linear unitssquare units

Excellent! Area is 2D space, perimeter is 1D length.

10. Find the area of a rectangle whose length is double its breadth and perimeter 36 cm.

Let breadth = b, length = 2bb

Perimeter = 2(2b + b) =

2 × 3b = 36 → b = cm

Length = cm

Area = 12 × = cm²

Perfect! Breadth=6cm, Length=12cm, Area=72cm².

Drag each formula to its correct shape:

Part A: Section B – Short Answer Questions (2 Marks Each)

1. Find the area and perimeter of a rectangle of length 9 m and breadth 4 m.

Area: l × b = × = m²

Perimeter: 2(l + b) = 2( + ) = 2 × = m

Perfect! Area = 36 m², Perimeter = 26 m.

2. Find the area and perimeter of a square whose side is 10 m.

Area: × = m²

Perimeter: 4 × = m

Excellent! Area = 100 m², Perimeter = 40 m.

3. The length of a rectangle is 8 cm, and its area is 48 cm². Find its breadth.

Area = l × b =

8 × b = 48

b = 48 ÷

b = cm

Great! Breadth = 6 cm.

4. Find the side of a square whose perimeter is 40 cm.

Perimeter = 4 × side =

Side = 40 ÷

Side = cm

Perfect! Side = 10 cm.

5. Find the area of a parallelogram whose base is 12 cm and height is 8 cm.

Area = base × height

= ×

= cm²

Excellent! Area = 96 cm².

6. Find the perimeter of an isosceles triangle whose equal sides are 8 cm and base is 6 cm.

Perimeter = + +

= cm

Great! Perimeter = 22 cm.

7. The area of a triangle is 24 cm², and its base is 8 cm. Find its height.

Area = (1/2) × base × height =

(1/2) × 8 × h = 24

4 × h =

h = cm

Perfect! Height = 6 cm.

8. Find the length of a rectangle if its breadth is 6 cm and perimeter 28 cm.

Perimeter = 2(l + b) =

2(l + 6) = 28

l + 6 =

l = cm

Excellent! Length = 8 cm.

9. The side of a square is 15 cm. Find its area and perimeter.

Area: × = cm²

Perimeter: 4 × = cm

Great! Area = 225 cm², Perimeter = 60 cm.

10. Find the base of a parallelogram whose area is 54 cm² and height is 9 cm.

Area = base × height =

base × 9 = 54

base = 54 ÷

base = cm

Perfect! Base = 6 cm.

Part A: Section C – Long Answer Questions (4 Marks Each)

1. A rectangular field is 40 m long and 30 m wide. Find: (a) Its perimeter (b) Its area.

(a) Perimeter:

Perimeter = 2(l + b)l × b

= 2( + )

= 2 ×

= m

(b) Area:

Area = l × b

= ×

= m²

Perfect! Perimeter = 140 m, Area = 1200 m².

2. The perimeter of a square park is 96 m. Find its area.

Perimeter = 4 × side =

Side = 96 ÷

Side = m

Area: side × side

= ×

= m²

Excellent! Side = 24 m, Area = 576 m².

3. Find the area of a parallelogram whose base is 12 m and height is 7 m.

Area = base × height

= ×

= m²

Great! Area = 84 m².

4. The sides of a triangle are 8 cm, 10 cm, and 12 cm. Find its perimeter and verify if it can be right-angled.

Perimeter:

= + +

= cm

Check if right-angled:

Largest side squared = ² =

Sum of squares of other sides = ² + ²

= + =

144 is not equal toequal to 164

Therefore, it is notis a right-angled triangle

Perfect! Perimeter = 30 cm, Not a right triangle.

5. The length and breadth of a rectangle are in the ratio 3:2, and its perimeter is 100 m. Find its area.

Let length = 3x, breadth =

Perimeter = 2(3x + 2x) =

2 × 5x = 100

10x =

x =

Length = 3 × 10 = m

Breadth = 2 × 10 = m

Area: 30 × = m²

Excellent! Length=30m, Breadth=20m, Area=600m².

Part B: Objective Questions - Test Your Knowledge!

Answer these multiple choice questions:

6. Area of square with side 12 cm =

(a) 144 cm² (b) 120 cm² (c) 24 cm² (d) 100 cm²

Correct! Area = 12 × 12 = 144 cm².

7. If perimeter of rectangle = 40 cm and length = 12 cm, breadth =

(a) 6 cm (b) 8 cm (c) 10 cm (d) 12 cm

Perfect! 2(12+b)=40 → 12+b=20 → b=8 cm.

8. Height of triangle whose area = 20 cm² and base = 8 cm is:

(a) 4 cm (b) 5 cm (c) 6 cm (d) 8 cm

Excellent! (1/2)×8×h=20 → 4h=20 → h=5 cm.

9. The shape with opposite sides parallel and equal is:

(a) Parallelogram (b) Trapezium (c) Triangle (d) Square

Correct! Parallelogram has opposite sides parallel and equal.

10. The sum of all sides of a figure is called:

(a) Area (b) Perimeter (c) Diagonal (d) Width

Perfect! Perimeter is the sum of all sides of a figure.

🌟 Excellent Progress! You've Mastered Intermediate Area and Perimeter!

Here's what you've learned:

• Parallelogram Properties:

  Formula:

  • Area = base × height
  • Height must be perpendicular to base
  • Similar to rectangle but not same

  Key Points:

  • Opposite sides parallel and equal
  • Height ≠ side length (usually)
  • Area depends on perpendicular height only

• Advanced Triangle Calculations:

  Area Formula:

  • Area = (1/2) × base × height
  • Height is perpendicular to base
  • Can use any side as base with corresponding height

  Finding Unknown:

  • Given area and base → height = (2 × area) ÷ base
  • Given area and height → base = (2 × area) ÷ height

• Ratio Problems:

  Method:

  • Let dimensions be in ratio a:b → use ax and bx
  • Use perimeter or area equation
  • Solve for x
  • Find actual dimensions

  Example:

  • Ratio 3:2, perimeter 100m
  • Length = 3x, breadth = 2x
  • 2(3x + 2x) = 100 → x = 10
  • Dimensions: 30m × 20m

• Finding Dimensions from Area/Perimeter:

  Square:

  • Given perimeter → side = P ÷ 4
  • Given area → side = √area

  Rectangle:

  • Given area and one side → other side = area ÷ known side
  • Given perimeter and one side → other side = (P÷2) - known side

• Units Conversion:

  • 1 m = 100 cm
  • 1 m² = 10000 cm²
  • 1 km = 1000 m
  • 1 km² = 1000000 m²
  • Always convert to same units before calculating

• Real-World Applications:

  • Fencing: Calculate perimeter
  • Flooring/Carpeting: Calculate area
  • Painting: Calculate area of walls
  • Gardening: Area for planting
  • Construction: Material estimation

• Problem-Solving Strategy:

  1. Read problem carefully
  2. Identify shape and what's given
  3. Write correct formula
  4. Substitute values
  5. Solve step by step
  6. Check if answer makes sense
  7. Write correct units

• Common Mistakes to Avoid:

  • Confusing base × height with side × side
  • Forgetting (1/2) in triangle area
  • Using slant height instead of perpendicular height
  • Wrong units in answer
  • Not simplifying ratios properly
  • Arithmetic errors in calculations

Mastering these concepts helps in everyday situations like home improvement and space planning!