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Measurement - Perimeter and area of rectangles and triangles

Grade 6IGCSE

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 2D shape, measured in linear units (cm, m, km).

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Area is the amount of surface covered by a 2D shape, measured in square units (cm², m², km²).

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The height of a triangle must always be the perpendicular height (at a 90-degree angle to the base).

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The perimeter of any polygon is found by adding the lengths of all its outer sides.

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For composite shapes, divide the shape into simpler rectangles or triangles to calculate the total area.

📐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}.