Video: Calculating the Area of a Composite Figure Involving a Triangle and a Rectangle

If 𝐸𝐹 = 4.5 cm, find the area of the given figure to the nearest hundredth.

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Video Transcript

If 𝐸𝐹 equals 4.5 centimeters, find the area of the given figure to the nearest hundredth.

So, the first thing we’re gonna do is mark on the value we know, so we’ve now got this measurement. So now, to find the area of the total given shape, what we wanna do is split it into two parts. So, we’ve got part A and part B. So, part A is a triangle and part B is a rectangle.

So first of all, if we take a look at the triangle, then we know that the area of a triangle is equal to a half multiplied by the base multiplied by the height. And it’s worth noting that the height is, in fact, the perpendicular height. So, it means it needs to be at right angles to the base. Well, if we look at the triangle we’ve got, then the area is gonna be equal to a half multiplied by 10 because that’s the length of the base. And that’s because the bottom section is a rectangle. So, therefore, 𝐷𝐴 is the same length as 𝐶𝐵. And then, this is multiplied by 4.5, which is our perpendicular height.

So, therefore, the area is gonna be equal to five multiplied by 4.5, which’s gonna give 22.5 centimeters squared. And that’s because if the five multiplied by four, that’s 20 and then five multiplied by 0.5 is 2.5. So that’s gonna give us 22.5.

So, then, next to work out the area of the rectangle, which is our section we’re gonna call B. We’re gonna use the formula for the area of a rectangle, which is length multiplied by width. So, this is gonna be equal to 10 multiplied by six, which is gonna be equal to 60 centimeters squared.

Okay, great. So, now, all we need to do to work out the total area is add these two values together. So, therefore, the total area is gonna be equal to 22.5 add 60, which is gonna give a total area of 82.5 centimeters squared.

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