Area of Figures
This wiki is incomplete.
Area is the quantity that expresses the extent of a two-dimensional figure or shape in the plane. The 2-dimensional regular polygons and the area of each of the polygon will be found in this wiki.
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 pairs 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 side length of the square, you may consider using this formula: \(\sqrt{\text{area}}=\sqrt{a\times a} = a,\) where \(a\) denotes the side length. The formula to find a square's area is shown below:
\(\text{Area}=a^2\) or \(\text{area}=\frac{d^2}2,\) where \(a\) is the side length and \(d\) is the diagonal length of the square.
The formula to find a square's perimeter is
\[\text{Perimeter} =4\times a.\]
Warm-up for squares (Includes area and perimeter):
1A.) If one side of a square is \(2\text{ cm},\) find the area of the square. \((\)The formula:is \(L \times B,\) where \(L\) is the length and \(B\) is the breadth.\()\)
Answer:
We have \[2\text{ cm} \times 2\text{ cm} = 4\text{ cm}^{2}.\ _\square\]1P.) If one side of a square is \(1.5\text{ cm},\) find the perimeter of the square. \((\)The formula is \(L \times 4,\) where \(L\) is the side length.\()\)
Answer:
We have \[1.5\text{ cm}\times 4 = 6\text{ cm}.\ _\square\]2A.) If the area of a square is \(16\text{ cm}^2,\) find the side length of the square. \((\)The formula is \(\sqrt{a},\) where \(\sqrt{a}\) is the square root of the given area.\()\)
Answer:
We have \[\sqrt{16\text{ cm}^2} = 4\text{ cm}.\]2P.) If the perimeter of a square is \(24\text{ cm},\) find the length of the square. \(\big(\)The formula is \(\frac{P}{4},\) where \(P\) is the perimeter.\(\big)\)
Answer:
We have \[\frac{24\text{ cm}}{4} = 6\text{ cm}.\ _\square\]
Rectangles
Relevant wikis: Properties of Rectangles, Rectangle's Area
Rectangles, similar to squares which you have learned in the previous section, are quadrilaterals, which means that they are four-sided figures. Its sum of angles is 360°. Since a rectangle has 2 different lengths of lines, it also has length and breadth, like a square. It has 2 pairs of parallel lines, and 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 \(2a + 2b.\)