# Area of Figures

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PS: Here are examples of great wiki pages — Fractions, Chain Rule, and Vieta Root Jumping

## Square

Relevant wiki: Properties of Squares

Squares are quadrilaterals which means that they are four-sided figures. Its sum of angles is **360°**. Since squares have **equal** length of sides and it has **2 pair of parallel lines**, we can conclude that each angle in a square is **90°**. If a question gives you the area of a square and requests that you find the length of the square, you may consider using this formula: \(√area\) (a*a = **area** where "a" denotes length of the side )The formula to find a **square's area** is shown as below:

\(area=a^2\)or\(area=d^2/2\)\(where\ a =length\ of\ the\ square\ and\ d=diagonal\ of\ the\ square\)

The formula to find a **square's perimeter** is shown as below:

\(perimeter=4\times a\)

## Warm-up for squares (Includes area and perimeter)

1A.) If one side of a square is 2 cm, find the area of the square. Formula: \(L \times B\)

- \(L\) means the length.
- \(B\) means the breadth.
Answer:

2 cm \(\times\) 2 cm = \(4 cm^{2}\)1P.) If one side of a square is 1.5 cm, find the perimeter of the square. Formula: \(L \times 4\)

- \(L\) means the length.
Answer:

1.5 cm \(\times\) 4 = \(6 cm\)2A.) If the area of a square is \(16cm^{2}\), find the length of the square. Formula: \(√a\)

- \(√a\) means the square root of the given area.
Answer:

\(√16 cm^{2}\) = 4 cm2P.) If the perimeter of a square is 24 cm, find the length of the square. Formula: \(\frac{P}{4}\)

- \(P\) means the perimeter.
Answer:

\(\frac{24 cm}{4}\) = 6 cm

## Rectangles

\(Relevant\) \(wiki\): Properties Of Rectangles

\(Relevant\) \(wiki\): Rectangle's Area

Rectangles, **similar to squares** which you have learnt in the previous content, **are quadrilaterals** which means that they are four-sided figures. Its sum of angles is **360°**. Since rectangles have **2 different lengths of lines**, it has also a **Length and breadth**, like a square. It has **2 pair of parallel lines**, we can conclude that each angle in a rectangle is** 90°**.

Properties of a rectangle.

Property 1. The diagonals of a rectangle bisect each other.

Property 2. The opposite sides of a rectangle are parallel.

Property 3. The opposite sides of a rectangle are equal.

Property 4. A rectangle whose side lengths are \(a\) and \(b\) has area \(ab sin 90°\) = \(ab\)

Property 5. A rectangle whose side lengths are \(a\) and \(b\) has perimeter \(2a + 2b\) .

## Triangles

## Trapezoids

## Rhombuses

## Parallelograms

## Circles

## Hexagons

## Pentagons

**Cite as:**Area of Figures.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/area-of-solid-figures/