Area of composite shapes

so we have the strange-looking shape here and then we're given some some of its dimensions we know that this side right over here has a has a length of 3.5 this side over here is 6.5 then we know from here to here is 2 and then from here to here is 7 and then they're giving us this dimension right over here is 3.5 and so given that let's see if we can find the area of this entire of this entire figure and I encourage you to pause the video right now and try this on your own so I assume you've given a go at it and there might be a few things that jump out at you immediately the first thing is that they have these two triangles up here they give us all of the dimensions for them or at least the they give us the base and the height for it which is enough to figure out the area if I had a triangle if I were if I had a rectangle that was 2 times 3.5 or 2 wide 2 units wide and 3.5 units high if add a rectangle like that if I had a rectangle like that we know that it would have an area of 2 times 3.5 now a triangle is just going to be or especially a triangle like this a right triangle is just going to be half of a rectangle like this we just care about half of its area so this area is going to be 1/2 times 2 times 3.5 and 1/2 times 2 is equal to 1 1 times 3.5 is 3.5 square units so the area of that part is going to be 3.5 square units now let's think about the area of this triangle right over here well once again we have its height is 3.5 its base is 7 so it's area is going to be 1/2 times 7 times 3.5 1/2 times 7 is 3.5 times 3.5 so this part is 3.5 and I'm going to multiply that times 3.5 again so let's figure out what that product is equal to so 3.5 times 3.5 5 times 5 is 25 3 times 5 is 15 plus 2 is 17 let's cross that out move one place over to the left 3 times 5 is 15 three times three is nine plus one is ten so that gets us to five plus five plus zero is 5 7 plus 5 is 12 carry the 1 1 plus 1 is 2 and we have a 1 and we have 2 digits to the right of the decimal 1 2 so we're gonna have two digits to the right of the decimal and the answer so the area here is 12.25 square units now this region might seem a little bit more maybe maybe a little bit more difficult because it's kind of this weird trapezoid looking thing but one thing that might pop out at you is that you can divide it very easily into a rectangle and a triangle and we can actually figure out the dimensions that we need to figure out the areas of each of these we know what the width of this rectangle is right or the length of this rectangle whatever you want to call it it's going to be 2 units plus 7 units so this is going to be 9 we know that this distance is 3.5 so if this distance right over here is 3.5 then this distance down here adds has to add up with 3.5 to 6.5 so this must be this must be 3 so now we can actually figure out the area so the area of this rectangle is just going to be its height times its length or nine times three point five nine nine times 3.5 and one way you could do it we could even try to do this in our head this is going to be 9 times 3 plus 9 times 0.5 so 9 times 3 is 27 9 times 0.5 that's just half of 9 so it's going to be 4.5 27 plus 4 we goes to 31 so that's going to be equal to 31 point 5 or you could multiply it out like this if you like but the area of this region is 31.5 and then the area of this triangle right over here it's going to be 9 times 3 times 1/2 we're looking at a triangle 9 times 3 is 27 27 times 1/2 is 13 13.5 and so to find the area of the entire thing we just have to sum up these areas so we have 30 1.5 31.5 plus thirteen point five thirteen point five plus 12.25 12.25 plus three point five plus three point five here so we just have a five here in the hundredths that's the only one 5 Plus 5 is 10 plus 7 is 17 1 plus 1 is 2 plus 3 is 5 plus 2 is 7 plus 3 is 10 1 plus 3 is 4 plus 1 is 5 plus 1 is 6 so we get a total area for this figure of 60 point 7 5 square units