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 Area of 2D Figures

Area of Triangle

Area = \frac{1}{2}\times base\timesheight

area of 2d figures

 The base and height of triangle should be perpendicular to each other.

Example: Find the area of triangle with base length 4 ft and vertical height 3 ft.

Area of triangle =\frac{1}{2\times4\times3=2\times3= 6 ft2

 

Area of Square

Area of a square = (side)2

area of 2d figures

Example: What is the area of square with each side length 2 yards?

Area of a square = (side)2 = (2)2 = 4 yd2

 

Area of Rectangle

Area of a rectangle = length × width

area of 2d figures
area of 2d figures

Example: What is the area of a rectangular sheet with length 8 inches and width 4 inches?

Area of rectangular sheet = length × width = 8
in × 4 in = 32 in2

Area of Parallelogram

Opposite sides in parallelogram are equal in length and opposite angles are equal in measure.

Area of parallelogram = base × height

 Example: What is the area of given parallelogram?

area of 2d figures

  Area of parallelogram = base × height = 4 mi × 3 mi = 12 mi2

Area of Trapezoid

A trapezoid has one pair of sides that are parallel to each other.

In the figure below, base 1 and base 2 are parallel to each other.

area of 2d figures

 

 

Area of trapezoid =\frac{1}{2}\times(base 1+base 2)\timesheight

Example: Find the area of a trapezoid with bases 7 cm and 3 cm. The height of trapezoid is 4 cm.

Area of trapezoid =\frac{1}{2}\times(7 cm + 3cm)\times 4cm= \frac{10}{2}  = 5 cm × 4 cm = 20 cm2

Check Point

  1. ABC is a right angled triangle with hypotenuse AC = 25 cm and base, BC = 24 cm. Find the area of triangle ABC.
  2. Find the area of a square field which is double the area of a rectangular field with length 60 m and 40 m.
  3. If the diagonal of a square is 10\sqrt{2} in, what is the area of square?
  4. What is the area of a trapezoid with height 3 in, and bases 1.5 in and 6.5 in?
  5. Find the area of parallelogram with base 7.5 yd and height 6.8 yd.
Answer key
  1. 84 cm2
  2. 4800 m2
  3. 100 in2
  4. 12 in2
  5. 51 yd2

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