The perimeter of a shape is calculated by adding up the length of all the sides or by measuring the outer boundary of a shape or an object. Some real-life uses of the perimeter are to know about the size of a photo frame, length of a lawn that for which we need to put a fence. Perimeters of small objects can be found by taking a string or a thread around the object for which perimeter is to be found. In the case of polygons, their perimeter can be found by adding up the sides of the polygon and expressing them in the given units.
The figure given below shows the perimeter of a square, which is 20 units. The following table lists the important differences between area and perimeter. The table given below lists some important formulas for the area and perimeter of some common shapes. Example 1: Find the area and perimeter of a square with a side length of 7 units. Example 2: The length of a rectangular carpet is 21 units. Its area is square units. Find the width of the carpet and the perimeter of the carpet. Area is defined as the measure of space occupied by any surface or object, whereas perimeter defines the length of the boundary of an object or a shape.
Perimeter is measured in linear units and area is measured in square units. For example, if the length and width of a rectangle are 6 units and 4 units respectively, then its perimeter is 20 units and the area of the rectangle is 24 square units. Perimeter is measured by calculating the length of the boundary of a surface or a shape. For a circle, the perimeter is referred to by the term 'Circumference'. The formulas you are going to look at are all developed from the understanding that you are counting the number of square units inside the polygon.
You can count the squares individually, but it is much easier to multiply 3 times 5 to find the number more quickly. And, more generally, the area of any rectangle can be found by multiplying length times width.
Find the area. Start with the formula for the area of a rectangle, which multiplies the length times the width. Substitute 8 for the length and 3 for the width. Be sure to include the units, in this case square cm. It would take 24 squares, each measuring 1 cm on a side, to cover this rectangle. Notice in a rectangle, the length and the width are perpendicular.
This should also be true for all parallelograms. Base b for the length of the base , and height h for the width of the line perpendicular to the base is often used.
Find the area of the parallelogram. Start with the formula for the area of a parallelogram:. Substitute the values into the formula. The area of the parallelogram is 8 ft 2. Find the area of a parallelogram with a height of 12 feet and a base of 9 feet. It looks like you added the dimensions; remember that to find the area, you multiply the base by the height. The correct answer is ft 2.
It looks like you multiplied the base by the height and then divided by 2. To find the area of a parallelogram, you multiply the base by the height. This would give you the perimeter of a 12 by 9 rectangle. The height of the parallelogram is 12 and the base of the parallelogram is 9; the area is 12 times 9, or ft 2.
Area of Triangles and Trapezoids. The formula for the area of a triangle can be explained by looking at a right triangle. Look at the image below—a rectangle with the same height and base as the original triangle.
The area of the triangle is one half of the rectangle! When you use the formula for a triangle to find its area, it is important to identify a base and its corresponding height, which is perpendicular to the base. A triangle has a height of 4 inches and a base of 10 inches. Start with the formula for the area of a triangle. Substitute 10 for the base and 4 for the height.
To find the area of a trapezoid, take the average length of the two parallel bases and multiply that length by the height:. An example is provided below. Notice that the height of a trapezoid will always be perpendicular to the bases just like when you find the height of a parallelogram. Find the area of the trapezoid. Start with the formula for the area of a trapezoid.
Substitute 4 and 7 for the bases and 2 for the height, and find A. The area of the trapezoid is 11 cm 2. Use the following formulas to find the areas of different shapes.
Working with Perimeter and Area. Often you need to find the area or perimeter of a shape that is not a standard polygon. Artists and architects, for example, usually deal with complex shapes. However, even complex shapes can be thought of as being composed of smaller, less complicated shapes, like rectangles, trapezoids, and triangles. To find the perimeter of non-standard shapes, you still find the distance around the shape by adding together the length of each side.
Finding the area of non-standard shapes is a bit different. Rectangle Formulas Examples 3. Triangle Formulas Examples 4. Circle Formulas Examples In the video lesson below we will cover harder examples using the given formulas to find the perimeter and area each shape.
Additionally, we will plot points on the coordinate plane and learn how to find specified distances using the Pythagorean Theorem or the distance formula, as well as finding unknown measurements given the area of a two-dimensional shape.
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