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
![Perimeter and Area of Rectangles](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fce822e18-852c-4c21-83fa-faa2c4f531a3-file.png&w=1080&q=75)
Image courtesy of Sphero
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=6cm and w=4cm.
P=2(6+4)=20cmArea of a Rectangle
The area A is the product of its length and width:
A=l×wExample:
Determine the area for l=5cm and w=3cm.
A=5×3=15cm2Perimeter and Area of Triangles
![Perimeter and Area of Triangles](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fbd55e066-bfb7-4481-b203-e5b3ae142c4c-file.png&w=1080&q=75)
Area of a Triangle
A triangle's area is half the product of its base b and height h:
A=21×b×hExample:
For a base of 10cm and a height of 4cm, the area is:
A=21×10×4=20cm2Perimeter and Area of Parallelograms
![Perimeter and Area of Parallelograms](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F7f7c9589-34ad-493c-bdbc-28b03474e386-file.png&w=1080&q=75)
Perimeter of a Parallelogram
The perimeter P involves adding the lengths of all sides, or twice the sum of adjacent sides a and b:
P=2(a+b)Example:
With a=5cm and b=3cm:
P=2(5+3)=16cmArea of a Parallelogram
The area A is found by multiplying the base b by the height h:
A=b×hExample:
For b=8cm and h=5cm:
A=8×5=40cm2Perimeter and Area of Trapeziums
Area of a Trapezium
The area A is half the sum of the lengths of the parallel sides (a and b) times the height (h):
A=21(a+b)×h![Area of a Trapezium](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F2c3cac54-fc73-4459-8d21-ec51c5c6e861-file.png&w=1080&q=75)
Example:
For parallel sides a=6cm, b=4cm, and height h=5cm:
A=21(6+4)×5=25cm2Perimeter of a Trapezium
To find the perimeter P, add the lengths of all four sides:
![Perimeter of Trapezium](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F302d9333-d010-42f5-a1e6-9260f4535c1b-file.png&w=1080&q=75)
Example:
Given sides of lengths 4cm, 3cm, 5cm, and 6cm:
P=4+3+5+6=18cmPractice Problems
Problem 1: Rectangle
Given: l=7cm,w=2cm
Find the area and perimeter.
Solution:
Area:
A=l×w=7×2=14cm2Perimeter:
P=2(l+w)=2(7+2)=18cmProblem 2: Triangle
Given: b=9cm,h=3cm
Calculate the area.
Solution:
A=21×b×h=21×9×3=13.5cm2Problem 3: Parallelogram
Given: a=6cm,b=4cm,h=3cm
Determine the perimeter and area.
Solution:
Perimeter:
P=2(a+b)=2(6+4)=20cmArea:
A=b×h=6×3=18cm2Problem 4: Trapezium
Given: a=8cm,b=5cm,h=4cm
Find the area.
Solution:
A=21(a+b)×h=21(8+5)×4=26cm2