krit.club logo

Mensuration - Perimeter and area of 2D shapes

Grade 11IGCSE

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

🔑Concepts

•

Definition of Perimeter: The total boundary length of a 2D shape.

•

Definition of Area: The total space occupied by a 2D shape in square units.

•

Properties of regular and irregular polygons.

•

Circle properties: Radius, diameter, and circumference.

•

Arc length and Sector area: Fractions of a circle based on the central angle θ.

•

Compound shapes: Calculating area by splitting complex shapes into simpler ones (rectangles, triangles, etc.).

•

Unit conversion: Understanding how linear unit conversions (e.g., 1m = 100cm) change for area (1m² = 10,000cm²).

📐Formulae

Square: Area=s2,Perimeter=4s\text{Square: Area} = s^2, \text{Perimeter} = 4s

Rectangle: Area=l×w,Perimeter=2(l+w)\text{Rectangle: Area} = l \times w, \text{Perimeter} = 2(l + w)

Triangle: Area=12×base×height\text{Triangle: Area} = \frac{1}{2} \times \text{base} \times \text{height}

Triangle (Trigonometric): Area=12absin⁡(C)\text{Triangle (Trigonometric): Area} = \frac{1}{2}ab \sin(C)

Parallelogram: Area=base×height\text{Parallelogram: Area} = \text{base} \times \text{height}

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

Circle: Area=πr2,Circumference=2πr\text{Circle: Area} = \pi r^2, \text{Circumference} = 2\pi r

Arc Length=θ360×2πr\text{Arc Length} = \frac{\theta}{360} \times 2\pi r

Sector Area=θ360×πr2\text{Sector Area} = \frac{\theta}{360} \times \pi r^2

💡Examples

Problem 1:

A sector of a circle has a radius of 6 cm and a central angle of 60°. Calculate the area of the sector and the length of the arc. (Use π = 3.142)

Solution:

Arc Length = (60/360) * 2 * 3.142 * 6 = 6.284 cm. Sector Area = (60/360) * 3.142 * 6^2 = 18.852 cm².

Explanation:

To find the arc length and sector area, we multiply the total circumference and total area of the circle by the fraction of the circle represented by the angle (60/360).

Problem 2:

A trapezium has parallel sides of length 8 cm and 12 cm. If the area of the trapezium is 50 cm², find its perpendicular height.

Solution:

50 = 1/2 * (8 + 12) * h => 50 = 1/2 * 20 * h => 50 = 10h => h = 5 cm.

Explanation:

Substitute the known values into the area of a trapezium formula: Area = 1/2(a+b)h. Solve the resulting linear equation for the unknown height (h).

Problem 3:

Calculate the area of a triangle where two sides are 7 cm and 10 cm, and the included angle between them is 30°.

Solution:

Area = 1/2 * 7 * 10 * sin(30°) = 1/2 * 70 * 0.5 = 17.5 cm².

Explanation:

When the perpendicular height is not given but an angle is, use the trigonometric area formula Area = 1/2 ab sin(C).