Learn about Perimeter and Area In this lesson, let’s learn how to use the formulas for perimeter and area of figures and we will use perimeter in an area and that’s what we’re going to compute for rectangles, triangles, etc. Before we start, let’s just cover the formulas on what do we do for areas and perimeters of different figures. So, let’s first look at a particular rectangle. So, we’re dealing with a rectangle. Let’s say this is the length of the rectangle which is L and the width of the rectangle which is W. Now, the perimeter of a rectangle is, or perimeter of any plain figure is the sum of all the sides. So, if you look at the sides in a rectangle, this is the length, this the length, width, and width. So, the sum of all the sides is L and L and W and W is twice length plus twice width because there are two sides each of length L and two sides with width W. The area of a rectangle is length times the width. Area is how many square units does the rectangle cover exactly? When we talk about a square, all four sides of a square are equal in length. So if we apply the same concept, the perimeter would be side plus side plus side plus side plus side. Perimeter is four times the side and the area is the length which is side times the width which is also side, S or S squared or S times S. When we look at a triangle, if this is A, B, and C and this is the height of the triangle, then the perimeter is A plus B plus C is the perimeter. The area of a triangle is ½ times the base of the triangle which is C in this case times the height of the triangle. It is also written as ½ times base times height where this is the base and this is the height. So, let’s use these formulas to compute what we’ve been given. First problem says we need to compute the area and perimeter of this figure. Well, the perimeter of this figure is, well, it’s a rectangle – so it’s two times length. Length is six inches plus two times width which is four inches and this is in inches. The perimeter is always in inches or a single unit. So, 2 times 6 is 12 plus 2 times 4 is 8 which is 20 inches. That’s the perimeter, 2 times 6 is twelve, 2 times four is 8. That’s 20 inches. The area of this rectangle is length which is six times the width which is four inches squared because it’s inch times inch is inches squared which is 24 inches squared. So, perimeter is 20 inches. The area is 24 inches squared. What we did was use this formula given to us. Let’s try the second problem. The second problem is a triangle. The formula for perimeter of a triangle is the length of all the sides which is 5x plus 6 plus x plus 4. Combining like terms, 5x and x gives us 6x; 6 and 4 gives us 10. So, the perimeter is 6x + 10. All I did was added the length of all three sides. The area of a triangle is 1/2 times the base – base is 6 times the height which is x plus 4 which is ½ times 6 is 3. So, 3 times x plus 4 or if I opened this up, 3 times x is 3x plus 3 times 4 is 12. So, the area of this triangle is 3x + 12 and this is the formula that we used. Now, let’s do the second problem which says find the perimeter and area of a square whose sides are 9.1 yards in length. So when we’re talking about a square and this is 9.1 yard and this is 9.1 yard, all four sides are equal in a square. So, what is the perimeter? Perimeter is 4 times the side length which is 4 times 9.1 yards which is 36.4 yards perimeter, 4 times S, that’s the formula we used. The area of a square is the square of the side. So, take any side multiply it with the same value which is 9.1 yard times 9.1 yard which is 82.81 yard squared. So, the area of the square is 82.81 yard square. All we did was multiply it, length times width or in this case side times side because both the sides are equal. So, the key thing that we’ve learned here is if we remember that the basic figures in geometry, rectangle, length times width is area, 2L plus 2W is the perimeter, side squared is the area and 4 times the length of the sides and in