## Area of Shapes

Geometric shapes are the figures with a set of points connected by lines resulting in a closed figure.

**For example**, triangle, square, rectangle and quadrilateral are shapes with 3 and 4 points connected by lines. Shapes with bounded curves don’t have sides but have the circumference.

Mirrors of different shapes with sides and curves.

**Area**

The area of a shape is the “space enclosed within the perimeter or the boundary” of the given shape. We calculate the area for different shapes using math formulas.

In the following pictures, the shaded region denotes the area for the respective shapes.

Name & Shape | Properties | Area |

Circle | The length between the center “o” to the point on the circumference is the radius “r” | A = πr2 π = 3.14 (constant) |

Triangle | One angle is the right angle | A = ^{1}⁄_{2} × Base × Height |

Square | All sides are equalEach angle is 90 degree | A = Length of Side^{2} |

Rhombus | All sides are equalOpposite sides are parallelOpposite angles are equal | A = p × q |

Rectangle | Opposite sides are equal and parallelEach angle is 90 degree | A = Length × Breadth |

Parallelogram | Opposite sides are equal and parallelOpposite angles are equal | A = Base × Height |

The “textured” region represents the area of the shape

## Unit of Measurement

The unit of measurement for the area is always the square of the unit in which lengths are given. The resultant unit is the product of the units of the given lengths.

Let’s take an example, the area of a square with side length 8 cm is:

Area = (Length of side)^{2}

Area = 8 cm × 8 cm

Area = 64 cm^{2}

**Application**

The application field of area formula is in architecture, land surveying, and map designing. The rescaled version of the area for a given place is useful in designing knowledge tools such as globes and geophysical maps. The area calculation for a two-dimensional shape is the first step to interpret the volume of a three-dimensional object such as cone, cylinder, ball, and cube.

Fun Facts1. The Babylonian clay tablets with scribes were used to study math and interpret the concept of area using formula during 1800-1600 BCE. 2. Egyptians built great pyramids using the area based properties and ratio between the surface area of sides and base area for a perfectly balanced structure |

**Related Math Vocabulary**

- Circumference
- Perimeter
- Quadrilaterals
- Circle
- Irregular and regular shapes

## Practice Problems

## Area of Shape## 1What is the area of a parallelogram with a base of 4 cm and a height 3 cm more than its base?12 square cm 14 square cm 24 square cm 28 square cm CorrectIncorrect Correct answer is: 28 square cm The height of the parallelogram = base + 3 cm, i.e., 4 cm + 3 cm or 7 cm. So, the area of the parallelogram = base ✕ height = 7 cm ✕ 4 cm or 28 square cm. ## 2What is the area of a rectangle with a width of 5 units and a length double its width?25 square units 30 square units 50 square units 100 square units CorrectIncorrect Correct answer is: 50 square units The length of the rectangle = 2 ✕ width, i.e., 2 ✕ 5 units or 10 units. So, Area of the rectangle = length ✕ width = 10 units ✕ 5 units or 50 square units. ## 3What is the area of a shape made by joining three squares of side 3 cm?6 square cm 9 square cm 18 square cm 27 square cm CorrectIncorrect Correct answer is: 27 square cm The area of a square is side ✕ side, i.e., 3 cm ✕ 3 cm or 9 square cm. So, the area of 3 such squares will be 3 ✕ 9 square cm or 27 square cm. ## 4What is the formula for the area of a circle with radius r?𝜋 ✕ r 2 ✕ 𝜋 ✕ r 𝜋 ✕ r ✕ r 2 ✕ 𝜋 ✕ r ✕ r CorrectIncorrect Correct answer is: 𝜋 ✕ r ✕ r The area of a circle is 𝜋 ✕ radius ✕ radius. |

## Frequently Asked Questions

**How do we find the area of irregular shapes if none of its sides are known?**

To find the area of an irregular shape, divide the shape into unit squares. Count the number of squares that cover the shape completely. If the shape does not occupy complete unit squares, estimate the number of unit squares that will fill it.

**Why is area a 2-dimensional quantity?**

The area of any shape is the space occupied by it on a plane surface. Therefore, area is a two-dimensional quantity as well.

**What is the area of a parallelogram?**

Area of a parallelogram = Base × Height

**What is the difference between area and volume?**

The space inside the boundary of a two-dimensional shape is known as area, whereas the space occupied by a 3-dimensional object is its volume.