Table of contents | |
Introduction | |
What are Shapes? | |
Types of Shapes | |
Difference Between 2D and 3D Shapes | |
What is Area? | |
Units of Measurement |
Imagine this: You are building with toy blocks—some are flat, like squares, and some are solid, like cubes. What if you could understand how these shapes work and how they fit together? That’s exactly what geometry teaches us! Let’s explore shapes and solids that make up the world around us.
Shapes are figures that describe the outline of objects. Some shapes are flat and have two dimensions, while others are solid and have three. Learning about these shapes helps us recognize, measure, and understand the structure of things around us.
Zero-Dimensional Shape (Point)
A point represents a position in space. It has no size, length, or width—just a spot or marker.
One-Dimensional Shape (Line)
A line has only one dimension—length. You can think of it as a path that extends endlessly in two directions.
Two-Dimensional Shapes (2D)
These shapes are flat and have two dimensions—length and breadth.
Three-Dimensional Shapes (3D Solids)
These shapes take up space and have three dimensions—length, breadth, and height.
The area is how much space a flat shape takes up.
Sol:
Length of board = 12 cm
Breath of board = 10 cm
Step 1: Calculate the area of the board
Area of board = length x breadth
⇒ Area of board = (10 x 12) cm²
⇒ Area of board = 120 cm²
Step 2: Calculate the area of one square sheetSide of sheet = 2 cm
Area of sheet = side × side
⇒ Area of sheet = (2 × 2) cm²
⇒ Area of sheet = 4 cm²
Step 3: Calculate the number of sheets required
Number of sheets required = Area of board / Area of sheet
⇒ Number of sheets required = 120 / 4
⇒ Number of sheets required = 30
Sol:
Let the breadth of the rectangle be x, and then the length will be 2x.
Area of rectangle = x × 2x = 512
⇒ 2x² = 512
⇒ x² = 512/2 = 256
⇒ x² = 256
⇒ x = 16
Thus, the breadth is 16 cm, and the length is 32 cm.
Sol:
Let a be the side of a square.
We know that the area of a square with side “a” = a²
So, a² = 289 cm² (given)
⇒ a = 17 cm
Hence, the measure of the side of the square is 17 cm.
Sol:
Area = 81 cm²
Area = side × side
⇒ 81 = (a)²
⇒ (9)² = (a)²
⇒ 9 cm = a
Perimeter = 4 × side
⇒ Perimeter = 4 × 9
⇒ Perimeter = 36 cm
Sol:
The perimeter of the bedsheet will be determined using the perimeter of the rectangle formula to determine the amount of lace required for the bedsheet’s border.
Given,
Length, l = 120 inches
Breadth, b = 95 inches.
As we know, the perimeter of a rectangle = 2(l + b) units.
Substituting the values in the formula, we get
Perimeter = 2(120 + 95) = 2 × 215 = 430 inches.
Hence, we will need 430 inches of lace to complete the border.
Example 3: Find the length of the sides of the square park, whose perimeter is 232 m.
Sol:
Perimeter of square park = 4 × side = 232 m
⇒ side = 232/4
⇒ side = 58 m.
Therefore, the length of the sides of the square park is 58 m.
A unit of measurement is a definite magnitude of a quantity that is adopted by law and is used as a standard for measuring the same type of quantity.
Millimeter (mm):
This is a tiny measurement, like the thickness of a paperclip wire.
Example: The width of a small button might be a few millimeters.
Centimeter (cm):
A bit bigger than millimeters, like the width of your fingernail.
Example: The length of a small toy car could be a few centimeters.
Meter (m):
This is bigger, like the height of a door or the length of a desk.
Example: The height of a basketball hoop is a few meters.
Kilometer (km):
A very large measurement, like the distance between your home and school.
Example: The distance from one town to another might be a few kilometers.
Square Millimeter (mm²):
Imagine a tiny square made by connecting four dots, each one a millimeter apart on each side.
Example: The area of a small sticker might be measured in square millimeters.
Square Centimeter (cm²):
A bit bigger than the square millimeter, like a small square on a piece of paper.
Example: The size of a postage stamp might be a few square centimeters.
Square Meter (m²):
Larger than the square centimeter, like the floor space in a room.
Example: The area of a small kitchen might be a few square meters.
Square Kilometer (km²):
This is very big, like the area of a city or a large park.
Example: The size of a big national park might be measured in square kilometers.
A drawing of a real object reduced or enlarged by a certain amount (called the scale).
Example: A garden with a paved border is shown below. 1 cm on this garden is equal to 100 m on the ground.
Rectangular Garden
Let’s find the length and breadth of the garden on the ground.
Consider two rectangles A and B having the same perimeter as 18 units.
Observe that both of them have different areas:
Hence, we conclude that:
If we cut any 2D figure, the area of that figure will be equal to the area of the pieces.
For example, if we cut a polygon into three pieces, the area of the polygon is equal to the sum of the areas of the three pieces.
Before Cutting
After Cutting
Area of a sheet of length 14 cm and breadth 5 cm = Sum of the area of five equal rectangles.
32 videos|57 docs|45 tests
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1. What are the main characteristics of 2D shapes? |
2. How can we differentiate between 2D and 3D shapes? |
3. What is the formula for calculating the area of common shapes? |
4. Why is understanding units of measurement important in geometry? |
5. What role do geometrical shapes play in everyday life? |
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