Need help? How to videos Why join? What is area? We explain what the term area means and how children are taught to calculate the area of a shape. Login or Register to add to your saved resources. Area is the term used to define the amount of space taken up by a 2D shape or surface. Area is calculated by multiplying the length of a shape by its width. The two sides cut right across many square units. Of course, a parallelogram is just a knocked-over rectangle.
So, mathematically, if we could cut off one end and attach it to the other, we would have the area in square units. We can do exactly that, since the area of a parallelogram with a base, b , and width or height, h , is found using this formula:.
If you divide a parallelogram along a diagonal, what do you have? Two triangles. That means the area of any triangle is half the area of a parallelogram with the same base length and height.
A parallelogram, remember, uses the same formula as a rectangle. The area of a triangle is, then, half the base, b , multiplied times the height, h :. Here is a right triangle, a sail from a foot Morgan sailboat with a base 20 1 4 feet and a height 44 1 2 feet. What is its area? The area of the triangle sail is approximately How about the home plate of an MLB baseball field? We can calculate the area of the home-plate pentagon by considering it as two shapes:.
Some two-dimensional shapes are not even polygons, like our ellipse, or a circle. The area of a circle with radius r is found using this formula:. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Let's learn how to calculate the area of different geometric shapes through examples and practice questions. The word 'area' means a vacant surface. The area of a shape is calculated with the help of its length and width.
Length is unidimensional and measured in units such as feet ft , yards yd , inches in , etc. However, the area of a shape is a two-dimensional quantity.
Hence, it is measured in square units like square inches or in 2 , square feet or ft 2 , square yard or yd 2 , etc. Most of the objects or shapes have edges and corners. The length and width of these edges are considered while calculating the area of a specific shape.
Let us see how to calculate the area of a shape with the help of a grid. The area of any shape is the number of unit squares that can fit into it. The grid is made up of many squares of sides 1 unit by 1 unit. The area of each of these squares is 1 square unit. Hence, each square is known as a unit square. Look at the figure shown below. Well, we already know that's 7 in this color. So it's that side right over there is of length 7. So it'll be 7 plus this length over here, which is going to be 5.
They tell us that. BC is 5. Plus 5. Plus DC is going to be the same length is AB, which is going to be 7 again. So plus 7. So plus 5 again. So you have 7 plus 5 is 12 plus 7 plus 5 is 12 again. So you're going to have a perimeter of And you could go the other way around.
Let's say that you have a square, which is a special case of a rectangle. A square has 4 sides and 4 right angles, and all of the sides are equal. So let me draw a square here. My best attempt. So this is A, B, C, D. And we're going to tell ourselves that this right here is a square. And let's say that this square has a perimeter. So square has a perimeter of So given that, what is the length of each of the sides? Well, all the sides are going to have the same length.
Let's call them x. All of the sides are congruent. All of these segments are congruent. They all have the same measure, and we call that x. So if we want to figure out the perimeter here, it'll just be x plus x plus x plus x, or 4x. Let me write that. They gave us that in the problem. And to solve this, 4 times something is 36, you could solve that probably in your head.
But we could divide both sides by 4, and you get x is equal to 9.
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