数学における面積とは？ 定義、公式、形、例

What is Area in Math? Definition, Formulas, Shapes, Examples Parents Explore by Grade Preschool (Age 2-5) Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Explore by Subject Math Program English Program More Programs Homeschool Program Summer Program Monthly Mash-up Helpful Links Parenting Blog Success Stories Support Also available on Educators Teach with Us For Teachers For Schools and Districts Data Protection Addendum Impact Success Stories Resources Lesson Plans Classroom Tools Teacher Blog Help & Support More Programs SpringBoard Summer Learning Our Library All By Grade Preschool Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 By Subject Math English By Topic Counting Addition Subtraction Multiplication Phonics Alphabet Vowels One stop for learning fun! Games, activities, lessons - it's all here! 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The space enclosed by the boundary of a plane figure is called its area . The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity. The term “area” refers to the space inside the boundary or perimeter of a closed shape . The geometry of such a shape contains at least three sides joined together to form a boundary. Symbolic representation of such space in mathematics refers to the “area” formula. To represent and draw real-life objects, designers and architects use different shapes such as circle , triangle , quadrilateral , and polygon . The invention of the wheel was the prime step of translating objects into geometric shapes . In the early days, the interpretation of “area” using a formula for geometric shapes evolved from the experiments conducted by Archimedes. Recommended Games Add to Find the Area Game Play Area of Composite Figure Game Play Area with Unit Squares and Side Lengths Game Play Area Word Problems on Product of Fractions Game Play Build the Area Game Play Determine the Area of Rectilinear Shapes Game Play Find Area by Multiplying Side Lengths Game Play Find Area in Square Units Game Play Find the Area by Multiplying the Side Lengths Game Play Find the Area of Shapes Using Unit Shapes Game Play More Games What is the formula of Calculating Area? We can calculate the area of a shape using a grid. The area of any shape is the number of square units that can fit into it. The grid is made of many squares and each square has sides 1 unit by 1 unit, i.e., the area of each square is 1 square unit. Each square is known as a unit square. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area . Now, imagine your square is made up of smaller unit squares. The area of a figure is counted as the number of unit squares required to cover the overall surface area of that particular 2-D shape. Square cms, square feet, square inches, square meters, etc., are some of the common units of area measurement. The easiest method to interpret the area of geometric shapes is using “unit squares”. A unit square is a square with each of its side length measuring 1 unit. Using this as a basis, the area of a polygon is the number of unit squares within a shape. To find out the area of the square figures drawn below, draw unit squares of 1-centimeter sides. Thus, the shape will be measured in $cm^{2}$, also known as square centimeters. Here, the area of the shapes below will be measured in square meters $(m^{2})$ and square inches $(in^{2})$. The area of a shape is the number of shaded unit squares. In the figure below, the number of shaded unit squares $= 24$. Hence, the area of the shape $= 24$ square units. How to calculate the area if there are also half unit squares in the grid? To understand that, let us take one more example: Step 1 : Count the full squares. There are 18 full squares. Step 2: Count the half squares. On counting, we see that there are 6 half squares. Step 3: 1 full square $= 1$ square unit So, 18 full square $= 18$ square units 1 half square $= \frac{1}{2}$ square unit 6 half squares $= 3$ square units Total area $= 18 + 3 = 21$ square units. Recommended Worksheets More Worksheets Origin of the Term: Area The term ‘area’ originated from Latin, meaning ‘a plain piece of empty land’. It also means ‘a particular amount of space contained within a set of boundaries’. More about Area Look at the carpet in your home. To buy a carpet that fits the floor, we need to know its area. Or the carpet will be bigger or smaller than the space! Some other instances when we need to know the area are while fitting tiles on the floor, painting the wall or sticking wallpaper to it, or finding out the total number of tiles needed to build a swimming pool. Formulas for Calculating Area We are surrounded by so many 2-D shapes: circle, triangle, square, rectangle, parallelogram, and trapezium. You can draw all of these shapes on your paper. Every shape is different and unique, so its area is also calculated differently. To find the area, first, identify the shape. Then, use the appropriate formula from the list given below to find its area. The area of an object can be explained as the amount of material required (such as paper, fabric, tiles) to cover the surface in a 2-dimensional plane. For 3-dimensional planes, such as cuboid, cube, sphere, etc., it is referred to as surface area. Areas of Composite Figures Every plane figure cannot be classified as a simple rectangle, square, triangle, or typical shape in real lif