| Square |
Area, A = a2 Where, a is the length of the sides of the square. |
| Rectangle |
Area of rectangle = width × height = w × h sq. units |
| Circle |
The area of a circle is A = $\pi$ × r2 |
| Triangle |
Area of a triangle = $\dfrac{1}{2}\left(b\times h\right)$ |
| Parallelogram |
Area of a parallelogram = base × height |
| Trapezoid |
Area of a Trapezoid = $\dfrac{1}{2}\left(a+b\right)\times h $ |
| Ellipse |
Area of ellipse = $\pi$ × a × b |
Area
Area is the space occupied by a surface or a flat-shape.
The area of a shape can be determined by counting the number of unit-squares required to completely cover the shape without overlapping.
The area is measured in square units.
Area of Plane Shapes
Square:
A Square is a flat shape with 4 equal sides and every angle is a right angle (90°)
If each side has the length a, the formula for the area A will be:
A = $a^{2}$
Example
Given a square where the length of each side (edge) is 5cm. Find the area of this square.
A=$a^{2}$
=$5^{2}$
=5 X 5
=25$cm^{2}$
Exercise:
Area of a square = length × length
= 27 × 27 sq. cm.
= 729 cm2.
Rectangle:
Opposite sides of a rectangle are parallel and equal in length.
All angles are equal to 90°.
A rectangle has the height h and the width w, we can find the area A, by multiplying its width and height together. Hence, we have:
A = wh
Example
Given a rectangle with the height of 4ft and the width of 3ft. Find its area.
A = wh
=3 X 4
=12$ft^{2}$
Exercise:
Height (h) of the rectangle = 12 ft.
width (w) of the rectangle = 3 ft.
Area of the rectangle = width × height
= 3 × 12
= 36 ft2
Circle:
A circle is a closed two-dimensional round shape with no corners or edges. All points on the circle are equidistant from the center of the circle.
A circle with the radius r, its area A, will be:
A = $ \pi r^{2}$
Where $\pi$ is constant that is approximately equals to 3.14.
Example
Given a circle with the radius 3cm. Find its area. Take $\pi$ = 3.14.
A = $ \pi r^{2}$
=(3.14)($3^{2}$)
=(3.14)(9)
=28.26$cm^{2}$
Exercise:
Radius = r = 3
Area= $\pi$ × r2
= $\pi$ × 32
= $\pi$ × (3 × 3)
= 3.14159... × 9
= 28.27 m2 (to 2 decimal places)
Triangle
A triangle has three sides and three angles.
The three angles always add to 180°
A triangle with the base b and height h, the area A, of the triangle is :
A=$\dfrac{1}{2}$bh
Example
Given a triangle with the base 4cm and the height 2cm. Find its area.
A=$\dfrac{1}{2}$bh
=$\dfrac{1}{2}$(4)(2)
=$\dfrac{1}{2}$(8)
=4$cm^{2}$
Exercise:
Height = h = 12
Base = b = 20
Area = $\dfrac{1}{2}\left(b \times h\right)$ =$ \dfrac{1}{2}\left(20\times 12\right)$ = 120
Parallelogram:
Opposite sides of a parallelogram are parallel and equal in length.
Opposite angles are equal in size.
For a parallelogram with the base b and the height h, the area A, is given as:
A=bh
Example
Given a parallelogram with the base 5in and the height 3in. Find the area of this parallelogram.
A=bh
=(5)(3)
=15$in^{2}$
Exercise:
Area = b × h
Area = 6 m × 3 m = 18 m2
Trapezoid (Trapezium):
A trapezoid with the height h and two parallel sides a and b, its area A, is given as:
A=$\left(\frac{a+b}{2}\right)h$
Example
Given a trapezoid with the height of 4in, and two parallel sides of 2in and 3in respectively. Calculate its area.
A=$\left(\frac{a+b}{2}\right)h$
=$\left(\frac{2+3}{2}\right)4$
=$\left(\frac{5}{2}\right)4$
=10$in^{2}$
Exercise:
Area = $\frac{1}{2}\left(a+b\right)\times h $
Area = $\frac{6m + 4m}{2} \times 3 $
= 5 m × 3 m = 15m2
Ellipse
The ellipse is a closed curve and is symmetric about the centre.
Major and Minor Axes:
The Major Axis is the longest diameter. It goes from one side of the ellipse, through the center, to the other side, at the widest part of the ellipse.
The Minor Axis is the shortest diameter (at the narrowest part of the ellipse).
The area of an ellipse is:
A=$\pi$ × a × b
where a is the length of the Semi-major Axis, and b is the length of the Semi-minor Axis.
Example:
Calculate the area of the ellipse where the major radius is 4 cm and minor radius is 3 cm.
A = $\pi$ a b
A = ($\pi$)(4)(3)
A = 37.68 cm2
Exercise:
Area of ellipse = $\pi$ × a × b
= 3.14 × 6 × 4
= 3.14 × 24
= 75.36m2