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Geometry and Measure - Area, perimeter and volume

Grade 7IGCSE

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

🔑Concepts

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Perimeter is the total distance around the boundary of a 2D shape, measured in linear units (mm, cm, m).

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

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Circumference is the specific name for the perimeter of a circle.

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Volume measures the 3D space occupied by an object, measured in cubic units (cm³, m³).

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Surface Area is the total area of all faces of a 3D solid.

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Compound shapes can be solved by splitting them into simpler rectangles or triangles.

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Ensure all measurements are in the same units before starting calculations.

📐Formulae

Perimeter of Rectangle=2(l+w)\text{Perimeter of Rectangle} = 2(l + w)

Area of Rectangle=l×w\text{Area of Rectangle} = l \times w

Area of Triangle=12×b×h\text{Area of Triangle} = \frac{1}{2} \times b \times h

Area of Parallelogram=b×h\text{Area of Parallelogram} = b \times h

Area of Trapezium=12(a+b)h\text{Area of Trapezium} = \frac{1}{2}(a + b)h

Circumference of Circle=2πr or πd\text{Circumference of Circle} = 2\pi r \text{ or } \pi d

Area of Circle=πr2\text{Area of Circle} = \pi r^2

Volume of Cuboid=l×w×h\text{Volume of Cuboid} = l \times w \times h

Total Surface Area of Cuboid=2(lw+lh+wh)\text{Total Surface Area of Cuboid} = 2(lw + lh + wh)

💡Examples

Problem 1:

A triangle has a base of 14 cm and a perpendicular height of 9 cm. Calculate its area.

Solution:

63 cm263 \text{ cm}^2

Explanation:

Apply the area of a triangle formula: A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}. Calculation: 12×14×9=7×9=63\frac{1}{2} \times 14 \times 9 = 7 \times 9 = 63.

Problem 2:

Find the circumference of a circle with a diameter of 10 cm. (Use π≈3.14\pi \approx 3.14)

Solution:

31.4 cm31.4 \text{ cm}

Explanation:

Using the formula C=πdC = \pi d, multiply the diameter by π\pi: 3.14×10=31.43.14 \times 10 = 31.4.

Problem 3:

A cereal box (cuboid) has dimensions 20 cm by 5 cm by 30 cm. Find its volume.

Solution:

3000 cm33000 \text{ cm}^3

Explanation:

Volume of a cuboid is found by multiplying length, width, and height: V=20×5×30=100×30=3000V = 20 \times 5 \times 30 = 100 \times 30 = 3000.

Problem 4:

Calculate the area of a trapezium where the parallel sides are 8 cm and 12 cm, and the height is 5 cm.

Solution:

50 cm250 \text{ cm}^2

Explanation:

Use the formula A=12(a+b)hA = \frac{1}{2}(a+b)h. First, add the parallel sides (8+12=208 + 12 = 20). Then, A=12×20×5=10×5=50A = \frac{1}{2} \times 20 \times 5 = 10 \times 5 = 50.