This section is dedicated to mastering the calculations involved in determining the perimeters and areas of fundamental geometric shapes: rectangles, triangles, parallelograms, and trapeziums. By engaging with the formulas and examples provided, students will develop a strong foundation in handling a variety of geometrical problems.

Perimeter and Area of Rectangles

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Perimeter of a Rectangle

The perimeter $P$ of a rectangle is twice the sum of its length $l$ and width $w$:

$P = 2(l + w)$

Example:

Calculate the perimeter of a rectangle where $l = 6 \, \text{cm}$ and $w = 4 \, \text{cm}$.

Area of a Rectangle

The area $A$ is the product of its length and width:

Example:

Determine the area for $l = 5 \, \text{cm}$ and $w = 3 \, \text{cm}$.

Perimeter and Area of Triangles

Area of a Triangle

A triangle's area is half the product of its base $b$ and height $h$:

Example:

For a base of $10 \, \text{cm}$ and a height of $4 \, \text{cm}$, the area is:

Perimeter and Area of Parallelograms

Perimeter of a Parallelogram

The perimeter $P$ involves adding the lengths of all sides, or twice the sum of adjacent sides $a$ and $b$:

Example:

With $a = 5 \, \text{cm}$ and $b = 3 \, \text{cm}$:

Area of a Parallelogram

The area $A$ is found by multiplying the base $b$ by the height $h$:

Example:

For $b = 8 \, \text{cm}$ and $h = 5 \, \text{cm}$:

Perimeter and Area of Trapeziums

Area of a Trapezium

The area $A$ is half the sum of the lengths of the parallel sides $(a \text{ and } b)$ times the height $(h)$:

Example:

For parallel sides $a = 6 \, \text{cm}$, $b = 4 \, \text{cm}$, and height $h = 5 \, \text{cm}$:

Perimeter of a Trapezium

To find the perimeter $P$, add the lengths of all four sides:

Example:

Given sides of lengths $4 \, \text{cm}$, $3 \, \text{cm}$, $5 \, \text{cm}$, and $6 \, \text{cm}$:

Practice Problems

Problem 1: Rectangle

Given: $l = 7 \, \text{cm}, w = 2 \, \text{cm}$

Find the area and perimeter.

Solution:

Area:

Perimeter:

Problem 2: Triangle

Given: $b = 9 \, \text{cm}, h = 3 \, \text{cm}$

Calculate the area.

Solution:

Problem 3: Parallelogram

Given: $a = 6 \, \text{cm}, b = 4 \, \text{cm}, h = 3 \, \text{cm}$

Determine the perimeter and area.

Solution:

Perimeter:

Area:

Problem 4: Trapezium

Given: $a = 8 \, \text{cm}, b = 5 \, \text{cm}, h = 4 \, \text{cm}$

Find the area.

Solution: