Understanding the concepts of area and perimeter is fundamental in mathematics. These concepts not only form the basis of geometry but also find applications in various real-world problems, including architecture, engineering, and everyday problem-solving. This comprehensive guide will explore the calculation and application of area and perimeter across different geometric shapes, focusing on squares, rectangles, circles, and triangles, often highlighted in examinations like the PSLE.
1. Area and Perimeter of Squares
A square is a four-sided polygon characterised by equal sides and right angles at each corner. Both the area and perimeter of a square are straightforward to calculate due to its symmetrical properties.
(Adapted from PSLE Paper 1 2022, Questions 28)
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.6 cm, 8.2 cm and 9.2 cm. What is the area of the square?
Solution:
Note: Do not be confused between perimeter and area of squares!
If you know what the perimeter of a square is, you can find the length of one side by dividing by 4.
2. Area and Perimeter of Rectangles
A rectangle is a four-sided polygon where opposite sides are equal in length and every angle is a right angle. The formulas for area and perimeter are similar to those of squares but adapted for differing lengths and widths.
Example:
(Adapted from PSLE Paper 2 2022, area and perimeter of rectangles questions 16)
A plot of land of area 876 cm2 is divided into three rectangular fields of equal width.
The fields are fenced using 177 m of fencing, indicated by …….. in the figure below.
(a) Find the length of AB.
(b) Find the perimeter of the plot of land.
Solution:
Tip: Fencing is indicated by ….., it is not the perimeter!
(a)
To find the length of the 2 blue lines, we need to first find the length of rectangle B.
To do that, since we know the total area, we need the area of Rectangles A and C to subtract from the total.
3. Area and Perimeter of Triangles
Example:
(Adapted from PSLE Paper 1 2021, Qn 23)
Find the area of the shaded triangle.
Solution:
Tip: The trick of such PSLE area questions is to identify the correct base and height. Always remember that the height of the triangle is perpendicular to the base.
4. Area and Perimeter of Circles
A circle is a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre). Calculating the area and perimeter (circumference) involves π (Pi), approximately equal to 3.14159.
Example:
(Adapted from PSLE Paper 2 2023, area and perimeter of circle questions 12)
(a) Find the perimeter of the shaded part.
(b) Find the area of the shaded part.
Solution:
Tip: The trick of such questions is to see how you can shift lines to make it a full circle. In this case, the perimeter of the shaded figure is actually the circumference of 3 circles.
Understanding the concepts of area and perimeter not only enhances mathematical proficiency but also prepares students to tackle practical area and perimeter questions and challenges in real-world settings and academic exams like the PSLE. Mastering these calculations helps in fields ranging from architecture to home decorating, enabling precise, efficient design and resource use. This knowledge fosters analytical thinking and a deeper appreciation for the structured yet creative application of geometry, illustrating how foundational mathematical principles are integral to both understanding and shaping the world around us.
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