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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 =  baseheight

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 = 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 =(base 1+base 2)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 =  = 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 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.
1. 84 cm2
2. 4800 m2
3. 100 in2
4. 12 in2
5. 51 yd2

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