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Measurement - Perimeter and area of rectangles and triangles

Grade 6Cambridge (IGCSE)

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

🔑Concepts

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Perimeter is the total distance around the outside of a shape. For a rectangle, it is the sum of all four sides: P=l+w+l+w=2(l+w)P = l + w + l + w = 2(l + w).

Rectangle diagram showing length and width labels for perimeter calculation.
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Area is the amount of space inside a 2D shape. For a rectangle, it is calculated by multiplying the length by the width (A=l×wA = l \times w).

Rectangle diagram indicating area is the space enclosed by the boundaries.
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The area of a triangle is half the area of a rectangle with the same base and height. The height MUST be the perpendicular distance from the base to the opposite vertex.

Triangle diagram showing base and perpendicular height.
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When calculating perimeter or area, ensure all measurements are in the same units (e.g., all cm or all m). Standard units for area are squared units like cm2cm^2 or m2m^2.

📐Formulae

Perimeter of a Rectangle: P=2(l+w)P = 2(l + w) or P=2l+2wP = 2l + 2w

Area of a Rectangle: A=l×wA = l \times w

Area of a Triangle: A=12×b×hA = \frac{1}{2} \times b \times h

Perimeter of a Triangle: P=a+b+cP = a + b + c

💡Examples

Problem 1:

Find the area and perimeter of a rectangle with a length of 8 cm and a width of 5 cm.

Solution:

Perimeter = 26 cm26\text{ cm}, Area = 40 cm240\text{ cm}^2

Explanation:

To find the perimeter, add length and width and multiply by 2: 2(8+5)=2×13=26 cm2(8 + 5) = 2 \times 13 = 26\text{ cm}. To find the area, multiply length by width: 8×5=40 cm28 \times 5 = 40\text{ cm}^2.

Problem 2:

A triangle has a base of 10 cm and a perpendicular height of 6 cm. Calculate its area.

Solution:

Area = 30 cm230\text{ cm}^2

Explanation:

Using the formula A=12×b×hA = \frac{1}{2} \times b \times h, we get 12×10×6\frac{1}{2} \times 10 \times 6. 10×6=6010 \times 6 = 60, and half of 60 is 30 cm230\text{ cm}^2.

Problem 3:

A rectangular garden has an area of 48 m248\text{ m}^2. If the length is 12 m12\text{ m}, find the width and then calculate the perimeter.

Solution:

Width = 4 m4\text{ m}, Perimeter = 32 m32\text{ m}

Explanation:

First, find the width using Area÷lengthArea \div length: 48÷12=4 m48 \div 12 = 4\text{ m}. Then calculate the perimeter using 2(l+w)2(l + w): 2(12+4)=2×16=32 m2(12 + 4) = 2 \times 16 = 32\text{ m}.

Problem 4:

Calculate the area of the right-angled triangle shown below, where the base is 12 cm12\text{ cm} and the height is 9 cm9\text{ cm}.

Right-angled triangle with base 12cm and height 9cm.

Solution:

A=12×b×hA = \frac{1}{2} \times b \times h A=12×12×9A = \frac{1}{2} \times 12 \times 9 A=6×9A = 6 \times 9 A=54 cm2A = 54\text{ cm}^2

Explanation:

To find the area of a triangle, identify the base and the perpendicular height. Substitute these values into the formula and multiply, then divide by 2.

Problem 5:

A square has a perimeter of 32 cm32\text{ cm}. Find the area of the square.

Square diagram with perimeter labeled 32cm.

Solution:

Step 1: Find the length of one side (ss): P=4sP = 4s 32=4s32 = 4s s=32÷4=8 cms = 32 \div 4 = 8\text{ cm}

Step 2: Calculate the area (AA): A=s×sA = s \times s A=8×8A = 8 \times 8 A=64 cm2A = 64\text{ cm}^2

Explanation:

A square has four equal sides. First, divide the perimeter by 4 to find the length of one side. Then, square that length to find the area.