Find the area of the given figure to the nearest hundredth.
Well, the first thing we need to do to solve this problem is divide our shape up. And we can do that by drawing a line down the middle. So we had a kite, but now what we’ve got are two identical triangles. And we know that the triangles are congruent or identical. And that’s because they have three lengths that are all the same.
So first of all, they have one length that we can identify here is the same. Then we’ve got another side, which is gonna be the same length of 6.16 centimeters. And then, finally, the hypotenuse of both of our triangles is shared. So therefore, this is gonna be the same length. So therefore, we confirmed that both of our triangles are identical or congruent. Okay, great, but how does this help us?
Well, we know that the area of a triangle is equal to a half 𝑏ℎ, where we’ve got a half multiplied by the base multiplied by the height. And the height is our perpendicular height. Well, in our triangles, we can call the base the 10.67 and then the perpendicular height the 6.16 because it’s at right angles to the 10.67. So therefore, we can say that the area of our total composite shape is going to be equal to two — and that’s because there are two triangles — multiplied by a half multiplied by 10.67 multiplied by 6.16.
Well, as we know that two multiplied by a half is equal to one, our area can be calculated by just multiplying 10.67 and 6.16. So our area is gonna be equal to 65.7272.
Well, have we finished? Is this how we want our answer left? Well, no, cause if we check the question, what we want is we want it left to the nearest hundredth. So therefore, the area is gonna be equal to 65.73 centimeters squared. And that’s because if we look at how we rounded it, if we look at the hundredth, this is the second decimal. So that’s the two. Well then the number after this, our deciding number, is seven. So because it’s five or above, we round the two to a three. So we get 65.73, and then it’s centimeters squared.