Area & Perimeter Of Regular Figures
In this course, we will cover how to find the area and perimeter of common figures such as trapeziums, parallelograms, and triangles. Students will also learn about the different parts of a circle, including the circumference, chord, sector, and segment, and how to calculate the area and circumference of a circle.
Related Lessons:
Area Of Trapezium and Parallelogram
Let us begin by reviewing the key properties used to identify a trapezium and a parallelogram, followed by a recap of the area formulas for both shapes.
A trapezium has the following key features:
- One pair of opposite sides are parallel to each other
- The other opposite pair must not be parallel
- Let the length of the parallel opposite sides be variable a and b, and let the height be h, and the height is perpendicular to a and b. The formula for trapezium will be \(\frac{1}{2} (π+π)Γβ\)
A parallelogram has the following key features:
- Opposite sides are parallel to each other for both sides
- Parallelogram is a “slanted rectangle”, so length of opposite sides are equal
- The base and height is perpendicular to each other and the area is \(πππ πΓβπππβπ‘\)
Area Of Triangle
The area formula of a triangle is usually one of the earliest formulas students learn in Mathematics. In fact, a triangle has exactly half the area of a parallelogram with the same base and height, which leads to its well-known formula:
Area Of Triangle=\(\frac{1}{2} baseΓheight\)
Semi-Circle, Quadrant, Chord, Sector & Segment
Let us now learn the different parts of a circle and understand their names & relationship to each other:
- Semi-Circle is when the diameter divides the circle into exactly 2 parts. Half of diameter is the radius
- Quadrant is when we cut the circle 4 parts. Each quadrant angle is 90Β°
- A chord is a line dividing the circle into 2 parts. The smaller part is known as the minor segment, and the larger part is known as the major segment.
- The smaller area encompassing the two radius and the arc is known as the minor sector, and corresponding larger sector is known as the major sector.
Formula For Circle, Segment & Sector
Now that we have learned the various parts of a circle, here are the key formulas related to different parts of a circle that students need to memorise:
- Area of circle\(=ππ^2\)
- Circumference of circle \(=2ππ\)
- Area of segment in a quadrant=\(=\frac{1}{4} ππ^2β\frac{1}{2} π^2\)
- Area of minor sector =\(\frac{x}{360}Γππ^2
\) - Arc length =\(\frac{x}{360}Γ2ππ
\)
Formula For Circle, Segment & Sector
In this video, we will learn how the formulas for the area of a trapezium, parallelogram, and triangle are connected, and understand how each formula is derived. By learning the relationship between these shapes and learning the step-by-step derivations, students will find it much easier to remember and apply the formulas.
The video will also introduce the different parts of a circle and explain how they are related. Finally, we will go through the key circle formulas, including the area and perimeter of sectors and segments, with clear explanations to strengthen students’ understanding.