Problem Set 50 – Area of Rectangles and SquaresClass 5 Maths · Chapter 12 Perimeter and Area · Problem Set 50 – Maharashtra Board

Summary: Problem Set 50 – Area of Rectangles and Squares

Area is the amount of surface inside a closed figure. We find it by counting how many unit squares fit inside.

A square of side 1 cm has an area of 1 square centimetre (1 sq cm). Big places use 1 sq m, and very big regions like districts use 1 sq km.

A rectangle 6 cm long and 4 cm wide holds 4 rows of 6 squares = 24 squares, so area of a rectangle = length × breadth.

A square of side 7 cm holds 7 rows of 7 squares, so area of a square = side × side = 49 sq cm.

To find a cost by area, multiply the area by the cost of 1 sq m.

Key points to remember

• Area = surface inside a closed figure
• Unit of area: sq cm, sq m, sq km
• 1 sq cm = area of a square of side 1 cm
• Rectangle: area = length × breadth
• Square: area = side × side
• Both sides must be in the same unit
• Cost = area × rate per sq m
• Perimeter uses cm; area uses sq cm

Problem Set 50 – Area of Rectangles and Squares – Notes

1. Counting squares

• Draw a shape on squared paper where each little square has sides of 1 cm.
• The number of whole squares inside is its area. A shape covering 8 small squares has area 8 sq cm.
• Area tells how much surface is covered; perimeter tells how long the border is.

2. Units of area

• A unit of length (cm) measures sides. To measure surface we need a unit square.
• 1 sq cm is the area of a square with 1 cm sides — good for a book cover or a tile.
• 1 sq m (a square with 1 m sides) is used for rooms, fields and playgrounds; 1 sq km is used for talukas, districts and cities.

3. Rule for a rectangle

• Split a rectangle 6 cm by 4 cm into 1 cm squares: you get 4 rows with 6 squares in each.
• 4 × 6 = 24 squares, so the area is 24 sq cm.
• Area of a rectangle = length × breadth. No need to draw the squares each time.

4. Rule for a square

• A square of side 7 cm has 7 rows of 7 squares: 7 × 7 = 49 sq cm.
• Area of a square = side × side.
• Two shapes can have the same perimeter but different areas: a 6 cm square (P 24 cm, A 36 sq cm) and a 9 cm by 3 cm rectangle (P 24 cm, A 27 sq cm).

5. Cost problems

• First find the area, then multiply by the cost of 1 sq m.
• Painting, flooring, carpeting and buying land are all charged by area.

Formulas at a glance

Key terms

Problem Set 50 – Area of Rectangles and Squares – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 50 – Area of Rectangles and Squares – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 50 – Area of Rectangles and Squares

⏱ About 30 minutes

1. Count (10 min)
   Draw rectangles on squared paper and count the squares inside each.
2. Learn the rules (10 min)
   See that rows × squares in a row = length × breadth; for a square, side × side.
3. Practise (10 min)
   Do the 4 'Try it yourself' problems, take the quiz and play 🎮 Play.