Determine, to the nearest tenth, the area of the given figure.
Well, to work out the area of the total figure, what we actually have are two separate shapes within. First of all, we’ve got the shape A, which is a triangle. And then we’ve got shape B, which is a trapezoid. So what we’re going to do is work out the area of each of our shapes, separately, and then add them together to give our total area.
Well, if we start with shape A, shape A is a triangle. And we’ve got a formula for that because the area of a triangle was equal to a half 𝑏ℎ, where 𝑏 is the base of the triangle and ℎ is, in fact, the perpendicular height of the triangle. So therefore, to calculate the area of shape A, what we’re gonna do is multiply a half by five, because this is the base of the triangle, by 4.3, which is the perpendicular height. And this is gonna give an area of shape A of 10.75, and then the units are centimeter squared.
So now what we can do is move on to shape B. Well, when we take a look at shape B, we can see that it’s a trapezoid. So therefore, what we have, in fact, for this is another formula. And that formula states that the area of a trapezoid is equal to a half multiplied by 𝑎 plus 𝑏 multiplied by ℎ. And this is where 𝑎 and 𝑏 are the parallel sides and ℎ is the distance between them.
So, in our shape B, our 𝑎 and 𝑏 are gonna be 4.3 and 3.3 because these are our parallel sides. And we know they’re parallel because we know that the angles at the bottom of each of them are right angles. And then, we’ve got our ℎ is 3.5, and that’s the distance between them. So therefore, the area of shape B is gonna be equal to a half multiplied by 4.3 plus 3.3 multiplied by 3.5. So this is gonna be equal to a half multiplied by 7.6 multiplied by 3.5. So therefore, we’re gonna get an area of shape B, which is equal to 13.3 centimeter squared.
So great! We have now found the area of shape A and the area of shape B. So what we need to do now to find the total area is add these together. So therefore, the total area is gonna be equal to 10.75 add 13.3, which is gonna be equal to 24.05 centimeter squared. Well, have we finished here? Well, not quite because if we look back at the question, we can see that it wants the answer to the nearest tenth. So what we need to do is round because we haven’t got the answer here to the nearest tenth.
Well, if we want to find it to the nearest tenth and we want to round, then what we’re gonna do is we look at the first decimal place because this is our tenth. Then, we look to the right of this, and this is our deciding number because this tells us whether we’re gonna round up or round down. Well, if it’s five or above, we round up. However, if it’s less than five, we round down. But as we can see, this is five. So what we’re gonna do is round up. So this is gonna give us a final answer for the total area of the given figure as 24.1 centimeter squared, and that’s to one decimal place or the nearest tenth.