Area and Perimeter of Irregular Shapes Tons of Examples

in this video we're going to focus on finding the area and the perimeter of regular shapes and figures so let's start with an example so let's say this section is 5 in or just simply five this part is six this part is five and this is 12 so let me just highlight specifically which parts are five and this part is six and here you have 12 go ahead and find the area and the perimeter of this irregular shape so let's start with the perimeter all we need to do is find the length of this side and this side so starting with the left side notice that it's simply 6 + 5 or 11 so that's 11 units long now let's find the length of this side so notice that we have 12 for the entire side and then this section is five five plus some number must add up to 12 to find that number it's just 12 - 5 so therefore this section has to be seven so now that we know it's seven we could find the perimeter we just have to add up all the numbers so it's going to be 5 + 6 which is 11 + 7 that's 18 18 + 12 is 30 30 + 11 that's 41 + 5 is 46 so therefore the perimeter of this figure is 46 units now let's the area of this figure so let's turn this into two rectangles so the area of this rectangle is simply length time width 5 * 6 so it's 30 square units now the area of the second rectangle is also length time width so it's 5 * 12 which is 16 now to find the total area we need to add up 30 + 60 and 30 + 60 is 90 so that's the area of this figure now let's work on another example so let's say actually let me draw different figure let's say we have rectangle attached to semicircle and it measures 5 in by 6 in find the area and the perimeter of this figure so let's start with the area the area of the rectangle is left time width which is going to be 30 square in now what about the area of semicircle notice that we have the diameter of the semicircle the diameter is 6 in long so if the diameter is 6 the radius is half of that half of 6 is three now the area of complete circle is pi 2 the area of semicircle or half of circle is 12 pi 2 so it's going to be 12 Pi * 3^ 2 where 3^ 2 is 9 half of 9 is 4.5 and to get decimal value let's multiply 4.5 by 3.14 so this is going to be about 14.1 so that's the area of the semicircle so the total area is 30 + 14.1 or 44.1 Square in now I'm going to redraw the same figure and this time we're going to calculate the perimeter so how can we find the perimeter of this figure well if the top side is five the bottom side it also has to be five the radius is still 3 units long so this time we need to find the circumference of the semicircle the circumference of complete circle is 2i for semicircle Circle it's half of 2i so it's simply PK so that's going to beunk * 3 so 3.14 * 3 that's about 9.42 that's the circumference of the semicircle so now to find the perimeter we just have to add up the four values 5 + 5 is 10 + 6 that's 16 and 16 + 9.42 that will give us the perimeter which is units let's work on another example so let's say if we have triangle attached to rectangle the rectangle is 8x4 the triangle has height of 4 units and let's say this side is six and this is five let's find the area first so the area of the rectangle is going to be length time width so 8 * 4 that's 32 now what about the area of the triangle the area of triangle is 12 base time height so the triangle has base that's 8 units long and it has height of 4 units so it's going to be 12 8 * 4 8 * 4 is 32 half of 32 is 16 so that's the area of the triangle so now the total area is going to be 16 + 32 so it's 48 square units for the entire figure now the last thing we need to do is calculate the perimeter if this side is four this side must be four so therefore we need to add up all five sides so it's going to be 4 + 5 + 6 + 4 + 8 4 + 5 is 9 6 + 4 is 10 9 + 10 that's 19 and so 19 + 8 is 27 so therefore it's 27 units long so that's the perimeter of the figure now let's move on to our next example let's put semicircle on top and triangle on the bottom so we're going to say this is seven this part is seven and 15 12 and 9 so go ahead and take minute pause the video and find the area and the circumference mean not the circumference but the area and the perimeter of this figure so let's start with the area let's make line now if this side is and this is therefore this section has to be 15 - 7 so it's 8 since 7 + 8 adds up to 15 so now we could find the area of this rectangle is it's going to be length * width so 12 * 8 12 * 8 is 96 we can also find the area of this rectangle as well now we need to know how long the rectangle is so notice that this side is 12 and this side is 7 therefore this side must be the difference of 12 and 7 so it's five so let's put 5 so now we can find the area of that rectangle it's going to be 5 * 7 which is 35 square units now we can find the area of the triangle it has height of eight and base of so the area of triangle is 12 base * height so that's 12 9 * 8 half of 8 is 4 4 * 9 is 36 so the area of the triangle is 36 square units now we could focus on the semicircle the area of semicircle is 12 pi squ so we got to find the radius if the diameter is five the radius is half of 5 so it's 2.5 2.5 squar that's about 6.25 if you multiply that by 3.14 that's going to give you about 19.625 and then times it by half this will give you an area of 9.81 125 which I'm going to round it and say it's about 9.8 so let's add up everything 96+ 35 + 36 + 9.8 that will give us total area of 176.832 so it's going to be < * 2.5 so 2.5 * 3.14 is excuse me is the circumference so that's going to be 7.85 units long now the only thing we need to do is find the hypotenuse of the right triangle we have base of height of eight and so to find the hypotenuse we can use the Pythagorean theorem A2 + B2 = c^2 so 9 + 8 2 that's equal to c^ 2 9 2 is 81 82 is 64 and if we add those two numbers that's going to give us 145 so is the square root of 145 which is about it's 12.04 but we can we'll write it just like that so now we need to add up everything to find the perimeter so we need to add 9 12 15 7.85 7 7 and 12.04 12 and 9 adds up to 21 and then once you add 15 that's 36 and then plus 7.85 and then if you add seven and seven and then 12.04 you should get perimeter of 69. 89 at least that's what got I'm going to double check my numbers just to make sure typed in everything correctly but that should be it 69.8 so now you know how to find the area and the perimeter of regular figures so just for review here's some formulas you need to know let's say if you have rectangle the area of rectangle is length time width the perimeter is simply the sum of all four sides it's 2 plus 2 next if you have triangle the area of triangle is base time height and if you have right triangle if you need to find Miss inside you can use the Pythagorean theorem and let's not forget to put the 1/2 in front of the base times height for triangle now the last other thing that we've considered is circle the area of circle is pi 2 and circumference is 2 pi and keep in mind the diameter is 2 and Pi if you round it is 3.14 now there are some other numbers after the four but in this example we just kept it simple and use 3.14 for semicircle everything is half the area is 12 pi r² and the circumference is just < but the diameter is still 2 so so this is not going to change so that's just recap of some of the formulat that we've used in this video so make sure you know those formulas if you have test on this stuff