Area of Parallelogram (Grade 5)
A parallelogram is a quadrilateral with two pairs of parallel sides. To find its area, we use its base and height — similar to a rectangle, but the height is not the same as the slanted side.
In Class 5, you will learn why the area of a parallelogram equals base times height, how this connects to the area of a rectangle, and how to solve related problems.
What is Area of Parallelogram - Class 5 Maths (Measurement)?
The area of a parallelogram is the amount of surface enclosed within its four sides.
The base is any one side of the parallelogram. The height (altitude) is the perpendicular distance between the base and the opposite side.
Area of Parallelogram = Base × Height
Why does this formula work?
If you cut a right triangle from one end of a parallelogram and move it to the other end, the parallelogram transforms into a rectangle with the same base and height. Since the area of a rectangle = base × height, the area of the parallelogram is also base × height.
Area of Parallelogram (Grade 5) Formula
Area = b × h
where b = base (one side) and h = height (perpendicular distance between the base and the opposite side).
Important:
- The height is NOT the slanted side — it is the perpendicular distance.
- Any side can be chosen as the base; the corresponding height changes, but the area remains the same.
Types and Properties
Special Cases:
- A rectangle is a special parallelogram where the height equals the side (since all angles are 90°). Area = length × breadth.
- A square is a parallelogram where base = height = side. Area = side × side.
- A rhombus is a parallelogram with all sides equal. Area = base × height (the height is NOT equal to the side unless it is a square).
Relationship with Triangle:
A diagonal divides a parallelogram into two equal triangles. So the area of each triangle = ½ × base × height.
Solved Examples
Example 1: Example 1: Basic Area Calculation
Problem: Find the area of a parallelogram with base 12 cm and height 7 cm.
Solution:
Step 1: Area = Base × Height
Step 2: Area = 12 × 7 = 84 cm²
Answer: The area is 84 cm².
Example 2: Example 2: Height vs Slant Side
Problem: A parallelogram has base 10 cm, slant side 6 cm, and height 5 cm. Find the area.
Solution:
Step 1: Area = Base × Height (NOT base × slant side).
Step 2: Area = 10 × 5 = 50 cm²
Answer: The area is 50 cm² (the slant side of 6 cm is not used).
Example 3: Example 3: Finding the Height
Problem: A parallelogram has area 96 cm² and base 16 cm. Find the height.
Solution:
Step 1: Area = Base × Height
Step 2: 96 = 16 × Height
Step 3: Height = 96 ÷ 16 = 6 cm
Answer: The height is 6 cm.
Example 4: Example 4: Finding the Base
Problem: A parallelogram has area 72 m² and height 8 m. Find the base.
Solution:
Step 1: 72 = Base × 8
Step 2: Base = 72 ÷ 8 = 9 m
Answer: The base is 9 m.
Example 5: Example 5: Word Problem - Painting
Problem: Aman wants to paint a parallelogram-shaped signboard with base 2 m and height 1.5 m. Paint costs ₹150 per sq m. Find the cost.
Solution:
Step 1: Area = 2 × 1.5 = 3 m²
Step 2: Cost = 3 × 150 = ₹450
Answer: The cost of painting is ₹450.
Example 6: Example 6: Comparing Rectangle and Parallelogram
Problem: A rectangle and a parallelogram both have base 8 cm and height 5 cm. Compare their areas.
Solution:
Step 1: Area of rectangle = 8 × 5 = 40 cm²
Step 2: Area of parallelogram = 8 × 5 = 40 cm²
Answer: They have the same area (40 cm²). A parallelogram with the same base and height as a rectangle has the same area.
Example 7: Example 7: Using Two Different Bases
Problem: A parallelogram ABCD has AB = 15 cm with corresponding height 8 cm, and AD = 12 cm. Find the height corresponding to AD.
Solution:
Step 1: Area using AB = 15 × 8 = 120 cm²
Step 2: Using AD as base: 120 = 12 × h
Step 3: h = 120 ÷ 12 = 10 cm
Answer: The height corresponding to AD is 10 cm.
Example 8: Example 8: Area of Rhombus as Parallelogram
Problem: A rhombus has side 13 cm and the perpendicular height between two parallel sides is 10 cm. Find the area.
Solution:
Step 1: A rhombus is a parallelogram. Area = base × height.
Step 2: Area = 13 × 10 = 130 cm²
Answer: The area is 130 cm².
Example 9: Example 9: Triangle from Parallelogram
Problem: A parallelogram has base 14 cm and height 9 cm. A diagonal divides it into two triangles. Find the area of each triangle.
Solution:
Step 1: Area of parallelogram = 14 × 9 = 126 cm²
Step 2: Each triangle = 126 ÷ 2 = 63 cm²
Answer: Each triangle has area 63 cm².
Example 10: Example 10: Doubling Dimensions
Problem: If both the base and height of a parallelogram are doubled, what happens to the area?
Solution:
Step 1: Original area = b × h
Step 2: New area = 2b × 2h = 4bh = 4 × original area
Answer: The area becomes 4 times the original.
Key Points to Remember
- Area of a parallelogram = base × height.
- The height is the perpendicular distance between the base and the opposite side, NOT the slant side.
- A rectangle is a special parallelogram where the height equals the side.
- A parallelogram and a rectangle with the same base and height have equal areas.
- A diagonal divides a parallelogram into two triangles of equal area.
- Any side can be taken as the base, but the corresponding perpendicular height must be used.
- If both base and height are doubled, the area becomes 4 times the original.
Practice Problems
- Find the area of a parallelogram with base 18 cm and height 10 cm.
- A parallelogram has area 108 cm² and height 9 cm. Find the base.
- A parallelogram has base 20 m, slant side 13 m, and height 12 m. Find the area. (Which measurement is NOT used?)
- Aditi cuts a parallelogram along a diagonal. Find the area of each triangle if the base is 16 cm and height is 7 cm.
- A rhombus has all sides 10 cm and height 8 cm. Find its area.
- A parallelogram PQRS has PQ = 24 cm with height 10 cm, and PS = 20 cm. Find the height corresponding to PS.
- If the height of a parallelogram is tripled and the base stays the same, by how much does the area increase?
- Kavi has a parallelogram-shaped plot with base 30 m and height 22 m. Find the area in square metres.
Frequently Asked Questions
Q1. What is the formula for the area of a parallelogram?
Area of a parallelogram = base × height, where the height is the perpendicular distance between the base and the opposite parallel side.
Q2. Why don't we use the slant side for the area?
The slant side is not perpendicular to the base. Area measures the space inside the shape, which depends on the perpendicular height, not the slant length.
Q3. Is the area of a parallelogram the same as a rectangle with the same base and height?
Yes. If a parallelogram and a rectangle have the same base and the same perpendicular height, their areas are equal.
Q4. How is the area of a parallelogram related to a triangle?
A diagonal divides a parallelogram into two equal triangles. Each triangle has area = ½ × base × height, which is half the parallelogram's area.
Q5. Can any side be the base?
Yes. You can choose any side as the base, but you must use the perpendicular height that corresponds to that base. The area will be the same regardless of which side you choose.
Q6. How do you find the height of a parallelogram?
If the area and base are known: height = area ÷ base. You can also measure the perpendicular distance between the two parallel sides directly.
Q7. Is a rectangle a parallelogram?
Yes. A rectangle is a special case of a parallelogram where all four angles are 90°. So the area formula (base × height) applies to rectangles too.
Q8. What happens to the area if only the base is doubled?
The area also doubles. New area = 2b × h = 2 × (b × h) = 2 × original area.
Q9. What is the difference between area and perimeter of a parallelogram?
Area = base × height (surface enclosed, in square units). Perimeter = 2 × (base + side) — the total boundary length, in linear units.
Q10. Is this topic in the NCERT Class 5 syllabus?
Yes. Area of a parallelogram is part of the Measurement chapter in NCERT/CBSE Class 5 Maths.
