krit.club logo

Measurement - Area of Squares, Rectangles, Triangles, and Parallelograms

Grade 6IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

The area of a square is the space inside its boundaries. Since all sides are equal (ss), the area is calculated by squaring the side length: A=s2A = s^2.

A square with side length s.
•

The area of a rectangle is found by multiplying its length (ll) by its width (ww). This represents the number of unit squares that fit inside the shape.

A rectangle showing length and width.
•

The area of a parallelogram is calculated using the base (bb) and the perpendicular height (hh). If you 'cut off' a triangle from one side and move it to the other, the parallelogram becomes a rectangle of the same area.

A parallelogram with base b and perpendicular height h.
•

The area of a triangle is exactly half the area of a rectangle or parallelogram with the same base (bb) and height (hh). Thus, A=12×b×hA = \frac{1}{2} \times b \times h.

A triangle with base b and perpendicular height h.

📐Formulae

AreaSquare=s2Area_{Square} = s^2

AreaRectangle=l×wArea_{Rectangle} = l \times w

AreaParallelogram=b×hArea_{Parallelogram} = b \times h

AreaTriangle=12×b×hArea_{Triangle} = \frac{1}{2} \times b \times h

AreaTriangle=b×h2Area_{Triangle} = \frac{b \times h}{2}

💡Examples

Problem 1:

A parallelogram has a base of 14 cm14 \text{ cm} and a perpendicular height of 9 cm9 \text{ cm}. Find its area.

Solution:

  1. Identify the formula for the area of a parallelogram: A=b×hA = b \times h
  2. Substitute the given values into the formula: A=14 cm×9 cmA = 14 \text{ cm} \times 9 \text{ cm}
  3. Multiply the numbers: 14×9=12614 \times 9 = 126
  4. State the final answer with square units: A=126 cm2A = 126 \text{ cm}^2

Explanation:

To find the area of a parallelogram, we multiply the base by the perpendicular height. We do not use the slanted side lengths if they are provided.

Problem 2:

Calculate the area of a triangle that has a base of 10 m10 \text{ m} and a height of 7 m7 \text{ m}.

Solution:

  1. Write down the triangle area formula: A=12×b×hA = \frac{1}{2} \times b \times h
  2. Plug in the base (1010) and height (77): A=12×10×7A = \frac{1}{2} \times 10 \times 7
  3. Multiply the base and height: 10×7=7010 \times 7 = 70
  4. Divide the result by 2: 70÷2=3570 \div 2 = 35
  5. Add the correct units: A=35 m2A = 35 \text{ m}^2

Explanation:

Since a triangle is half of a rectangle/parallelogram with the same base and height, we calculate the product of the base and height and then divide by two.

Problem 3:

A square photo frame has a side length of 12 cm12 \text{ cm}. Calculate the total area of the frame.

Square with side length 12 cm.

Solution:

Area=s2Area = s^2 Area=12 cm×12 cmArea = 12 \text{ cm} \times 12 \text{ cm} Area=144 cm2Area = 144 \text{ cm}^2

Explanation:

Since the shape is a square, we multiply the side length by itself to find the area.

Problem 4:

Find the area of a rectangle that has a length of 15 m15 \text{ m} and a width of 6 m6 \text{ m}.

Rectangle with length 15 m and width 6 m.

Solution:

Area=l×wArea = l \times w Area=15 m×6 mArea = 15 \text{ m} \times 6 \text{ m} Area=90 m2Area = 90 \text{ m}^2

Explanation:

To find the area of a rectangle, multiply the length by the width.