Area of 2D Figures

In geometry, the area of a two-dimensional (2D) figure refers to the measure of the amount of space enclosed by the figure. It is typically measured in square units, such as square centimeters (cm²) or square meters (m²). The concept of area is fundamental in various mathematical and real-world applications.

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Area of Triangle

Area = $\frac{1}{2}\times$ base $\times$ height

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

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Area of Square

Area of a square = (side)²

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

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 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 trapezoid = $\frac{1}{2}\times$ (base 1+base 2) $\times$ height

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

ABC is a right angled triangle with hypotenuse AC = 25 cm and base, BC = 24 cm. Find the area of triangle ABC.
Find the area of a square field which is double the area of a rectangular field with length 60 m and 40 m.
If the diagonal of a square is $10\sqrt{2}$ in, what is the area of square?
What is the area of a trapezoid with height 3 in, and bases 1.5 in and 6.5 in?
Find the area of parallelogram with base 7.5 yd and height 6.8 yd.

Answer key

84 cm²
4800 m²
100 in²
12 in²
51 yd²

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