Composite Area Problems 05:27 minutes

Video Transcript

Transcript Composite Area Problems

A rap battle is going on right here! Notorious C.A.T.'s rap game is on fleek. But, is he ready to take down his rival, MC Monta? We’re finally going to find out who’s the best rapper on the block. But, before they start spittin' rhymes Monta tries to intimidate C.A.T. with his bling. Monta brags that the chains he's wearing got more ice than Antarctica. Since bling's the thing C.A.T. wants to ice out his pendant like Monta. To figure out the area of his pendant that he needs to be covered in diamonds and shut down all the haters he’ll need to solve complex composite area problems. Let’s take a look at Notorious C.A.T.’s pendant. Whaaaat?! It’s in the shape of a cat?! I guess the cat's where it's at! To calculate the area, we’ll need to break down the composite shape into familiar geometric shapes. So, what do we know? Notorious C.A.T.'s pendant is composed of 2 isoceles right triangles 1 rectangle a semicircle and 2 emerald circles...you know...for the eyes. We don’t know all the measurements, but let's check out what we do know: We know that the total height of the pendant is 9 inches and the total width is 6 inches. The height of each isoceles right triangle ear is 2 inches and the radius of each circular eye is 1 inch. If these are the measurements we know, what dimensions do we need next? If the total width is 6 inches, how long is the radius of the semicircle? If you said 3 inches, you're exactly right! Also, notice that, since the total height of the pendant is 9 inches... We can subtract the known values from the total height of the pendant to find the height of the rectangle. And since the radius of the semicircle is 3 inches and the height of the triangle ears is 2 inches gives us 4 inches for the rectangle. Now, we’re ready to calculate the area of each shape. Do you remember how to find the area of a triangle? Yup! To find the area of any triangle, you multiply one half times the base times the height. Since Notorious's pendant has ears shaped like isoceles right triangles, we know that the length of the legs are each 2 inches long. Substituting the values for the triangle's base and height the area of EACH isoceles right triangle is 2 square inches... Now, on to the rectangular part of the face and we know that the area of a rectangle is width times height we can substitute 6 inches for the width and 4 inches for the height. Multiplying these together gives us the total area of the rectangular face. 24 square inches The cat pendant has emeralds for eyes already so we have to subtract the area of the eyes from the total area to know how much we need to cover using diamonds. But, how much area does each emerald eye take up? We already know that the area of a circle is pi times the squared radius Because the radius of each eye is 1 inch. The area of each emerald is equal to one pi square inches. The final part of the pendant is the semicircle. A semicircle is half of a circle so we can use the formula for area of a circle and simply multiply it by one half! We can see here that the radius is 3 inches. Therefore let's substitute the 3 inches. Simplified this results in nine pi over two square inches. We could also write this as 4.5π square inches. Finally, to calculate the area of the composite cat shape, we add and subtract the areas of the components we found. Substituting the known areas. Don't say just think. Area ears, area face, multiplying the ears and eyes by two combining like terms and then using the approximation 3.14 for π at the end to eliminate rounding errors results in the total area of the composite shape being approximately 35.85 square inches. Let's get back to reality and the battle of the bling. Monta don't care how much ice Notorious C.A.T. is rockin' because he's got the high quality gold and diamonds. It's delivery day and C.A.T. goes to check out his new pendant. MC Monta's jaw's gonna drop when he gets a load of this. Yo...for realz? His bling be made outta...chocolate!