Class 7 — Mathematics (NCERT)
Perimeter and Area of Triangles, Parallelograms, and Circles
Class 7
- ✓By the end of this lesson students will be able to define perimeter and area.
- ✓By the end of this lesson students will be able to calculate the perimeter and area of triangles.
- ✓By the end of this lesson students will be able to calculate the perimeter and area of parallelograms.
- ✓By the end of this lesson students will be able to calculate the circumference and area of circles.
- ✓By the end of this lesson students will be able to apply the concepts of perimeter and area to solve simple real-life problems.
Key concepts
The perimeter of a closed plane figure is the total length of its boundary. It is measured in units of length (e.g., cm, m).
The area of a closed plane figure is the measure of the surface enclosed by its boundary. It is measured in square units (e.g., cm², m²).
A polygon with three sides. The 'base' is any side of the triangle, and the 'height' is the perpendicular distance from the opposite vertex to that base.
A quadrilateral with two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal. The 'base' is any side of the parallelogram, and the 'height' is the perpendicular distance between the base and its opposite parallel side.
A simple closed curve, all points of which are at the same distance from a fixed point called the centre. The 'radius' (r) is the distance from the centre to any point on the circle. The 'diameter' (d) is the distance across the circle passing through the centre (d = 2r). The constant 'pi' (π) is approximately equal to 22/7 or 3.14.
Key facts to remember
- 1Perimeter is the total length of the boundary of a closed figure.
- 2Area is the measure of the surface enclosed by the boundary of a closed figure.
- 3Area of a Triangle = (1/2) × base × height.
- 4Area of a Parallelogram = base × height.
- 5Circumference of a Circle = 2πr or πd.
- 6Area of a Circle = πr².
- 7The value of π is approximately 22/7 or 3.14.
- 8Units for perimeter/circumference are linear (e.g., cm, m), while units for area are square units (e.g., cm², m²).
Worked examples
Example 1
Find the area of a triangle whose base is 12 cm and the corresponding height is 7 cm.
Answer
The area of the triangle is 42 cm².
Example 2
A parallelogram has a base of 8.5 m and its corresponding height is 4 m. Find its area.
Answer
The area of the parallelogram is 34 m².
Example 3
Find the circumference and area of a circle with a radius of 14 cm. (Use π = 22/7).
Answer
The circumference of the circle is 88 cm and its area is 616 cm².
Always remember to use the correct units for circumference (length) and area (square units).
Common mistakes
- ✗Confusing the formulas for perimeter/circumference and area.
- ✗Using diameter instead of radius (or vice-versa) in circle formulas without proper conversion (d = 2r).
- ✗Forgetting to include units or using incorrect units (e.g., cm for area instead of cm²).
- ✗Mistaking a side of a triangle/parallelogram for its height, especially when the height is an internal or external perpendicular.
- ✗Calculation errors, particularly when dealing with fractions (like 1/2) or the value of π.
Exam tips
- ★Always draw a neat diagram if one is not provided, marking the given dimensions clearly.
- ★Write down the correct formula before substituting the values.
- ★Show all steps of your calculation clearly and logically.
- ★Pay close attention to the units given in the problem and ensure your final answer has the correct units.
- ★Double-check your calculations, especially when dealing with multiplication and division.
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