Is A Square A Regular Quadrilateral – The area of a square is the area inside it. Let’s remember what a square is. A square is a closed shape bounded by four lines. A square can be regular or irregular. A regular square is a square whose sides are all the same length. A square that is not regular is called an irregular square. There are 6 types of squares.
On this page we will see how to find the area of a square by dividing a square into two triangles and how to find the area of a square by its four sides. Also, we will learn the formulas to find the area of each of these types of rectangles.
Is A Square A Regular Quadrilateral
The area of a square is nothing but the area enclosed by the sides of the square. It is measured in square units such as m
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, etc. The process for finding the area of a square depends on its type and the available information about the square. If the square does not belong to any of the above types, we can find its area by dividing the two triangles or using the formula (called the Bretschneider formula) to find the area of the square. with four sides. Here are formulas to find the area of a square that doesn’t belong to a standard type.
Consider a quadrilateral ABCD where the length of the diagonal BD is known as “d”. ABCD can be divided into two triangles by the diagonal BD. To find its area, we need to know the heights of triangles ABD and BCD. Let’s assume that the altitudes of the triangles BCD and ABD are given as (h_1) and (h_2), respectively. We find the area of square ABCD by adding the areas of triangles BCD and ABD.
From the figure above, the area of rectangle ABCD = area of ΔBCD + area of ΔABD.
So the area of the square ABCD = (1/2) × d × (h_1) + (1/2) × d × (h_2) = (1/2) × d × ((h_1+ h_2 )).
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Hence the formula used to find the area of a rectangle given one of its diagonals and the height of the triangle (made by the diagonal) is,
Given the sides of a square and its two opposite angles, we can find its area using Bretschneider’s formula. Imagine a square whose sides are a, b, c and d and whose two opposite angles are θ(_1) and θ(_2).
According to Heron’s formula, the area of a triangle with 3 sides a, b and c is (sqrt), where ‘s’ is the semicircle of the triangle, so s = (a + b + c) /2. To find the area of a square using Heron’s formula,
We have already learned that there are 6 types of squares namely square, rectangle, parallelogram, trapezoid, rhombus and kite. We have a special formula to find the area of each of these rectangles. let’s see her
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The area of a rectangle can be calculated if the coordinates of its vertices are known. Let’s consider a rectangle in the coordinate plane as shown below,
To find the area of the rectangle ABCD, we take the vertices A(x(_1), y(_1)), B(x(_2), y(_2)), C (x). (_3), y(_3)) and D(x(_4), y(_4)) of square ABCD and write them as shown below,
Note: We can also calculate the area of a rectangle using the coordinates of the vertices by dividing it into two triangles and adding their areas. Let’s understand this technique using the example given below,
Example: Consider the following four points: A(−3, 1), B(−1, 4), C(3, 2), D(1, −2). These four points are the points of the square:
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Here we divide the square into two triangles (using one of the diagonals), calculate the (positive value) of the areas of each triangle and add these values to get the total area. In the figure below, quadrilateral ABCD is divided into ΔABD and ΔADC.
= (1/2) |−3 × (4 − 2) + (−1) × (2 − 1) + 3 × (1 − 4)| = (1/2) |−6 −1 −9| = (1/2) × 16 = 8 square units
Math will no longer be a difficult subject, especially when you combine concepts with ideas.
The area of a square is the area that bounds it. It is measured in square units as in
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The area of a square is obtained by dividing the two triangles by a diagonal. Knowing the length of the diagonals and the height of the two triangles, the area (A) of the rectangle is A = (1/2) × diagonal × (subtracting the heights).
We know that the area of a square is found by dividing it into two triangles using a diagonal. Also, we know that the area of a triangle with 3 sides can be found by Heron’s formula. According to Heron’s formula, the area of a triangle with sides a, b, and c is given by (sqrt), where ‘s’ is the semicircumference of the triangle. ie s = (a + b + c)/2. Using this formula we can find the areas of two triangles (formed from a square) and add them together to get the area of the square.
If the points of a rectangle are given in coordinates, then first find the 4 side lengths and the length of one diagonal using the distance formula. Then divide the square in two using the function you found, use Heron’s formula to find the area of each triangle, and then add the areas of the two triangles to get the area of the square. somewhere The easiest and quickest way to learn squares is to build your own.
Find four correct objects to use as line segments (four = square; side = side). Anything goes, and they don’t have to be the same length: ruler, ruler, dowel, pencil – whatever you have on hand. If you connect four linear objects at their eight ends, you have a square, a four-sided polygon.
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You may have lined up the four sides to make the shape look complete, which means you created a rectangle. The four parts of your lines may have formed a sharp shape like an arrowhead; You’ve made a solid square.
Usually the four sides do not intersect, forming a simple square. You can arrange your square so that the line segments cross: you have a complex square.
A square has 4 right sides. Sides and angles can be equal or unequal. When two or four sides are the same, you get special types of squares like trapezoids and rectangles.
Two sides of a square can intersect – a composite square – making your square look like two triangles.
Ex 5.7, 3
Use a ruler or ruler to draw a rectangle. Draw four line segments such that each point covers a different endpoint. Whether you drew a simple or complex square, square or square, you’ve got it right!
Draw a simple rectangle. Don’t let any parts of the line overlap. Your simple rectangle can be broken or curved. If the two sides are facing in, you have drawn an oblong square.
Now draw a rectangle where two non-adjacent line segments intersect. You have drawn a complex square.
Each vertex is given a letter that, like a square, leads to the next vertex in either direction (clockwise or counterclockwise).
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A simple square is also known as a rectangle or square. A simple rectangle is symmetric if it has at least one pair of congruent sides.
All congruent quadrilaterals have one of their diagonals outside their circumscribed space. All complex squares have diagonals outside of their closed space.
You may have noticed that a complex square has self-intersecting sides. In mathematics, however, angles formed by points of intersection are not part of a shape.
A complex quadrilateral has two acute interior angles and two interior reflection angles. These two angles of reflection appear bulky, which can be confusing. They are still considered “interior angles”.
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Although two line segments intersect and appear to form two additional interior angles, a rectangle is still said to have only four interior angles. Self-intersecting line segments do not add two angles to a complex quadrilateral.
In this lesson you learned that a square is a planar figure with four line segments closed in space. Special types of squares, such as rectangles, trapezoids, and squares, have more restrictive definitions.
Malcolm has a master’s degree in education and holds four teaching credentials. He has been a public school teacher for 27 years and a math teacher for 15 years.
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