Question Video: Finding the Area of a Composite Figure Consisting of Triangles and a Trapezoid Mathematics • 6th Grade

Given that 𝐵𝐴 = 18 cm, 𝐴𝐶 = 27 cm, 𝐴𝐷 = 18 cm, 𝐷𝐸 = 50.4 cm, 𝐷𝐺 = 27 cm, 𝐺𝐹 = 36 cm, and 𝐺𝐻 = 27 cm, find the area of 𝐵𝐸𝐹𝐻𝐶 to the nearest hundredth.

04:54

Video Transcript

Given that 𝐵𝐴 equals 18 centimeters, 𝐴𝐶 equals 27 centimeters, 𝐴𝐷 equals 18 centimeters, 𝐷𝐸 equals 50.4 centimeters, 𝐷𝐺 equals 27 centimeters, 𝐺𝐹 equals 36 centimeters, and 𝐺𝐻 equals 27 centimeters, find the area of 𝐵𝐸𝐹𝐻𝐶 to the nearest hundredth.

So in this problem, the first thing we need to do is mark on all the different lengths that we’ve been given. So first of all, we have 𝐵𝐴 equals 18 centimeters. Then we have 𝐴𝐶 equals 27 centimeters. 𝐴𝐷 equals 18 centimeters. 𝐷𝐸 equals 50.4 centimeters. Then we’ve got 𝐷𝐺 and 𝐺𝐻 both 27 centimeters. And then finally, we have 𝐺𝐹 which is 36 centimeters. Okay, great. So we now have all our different lengths marked on our diagram. So what we’re gonna do to enable us to find the area of the total shape is divide it into five smaller pieces. So I’ve labeled them here, 1, 2, 3, 4, and 5. And what we’re gonna do is work out the area of each one of these individually. And then we’re gonna add them all together.

So first, we’re gonna look at shape 1 which is a triangle. Well, to find the area of triangles, what we have is a formula. And that is that the area of a triangle is equal to a half multiplied by the base multiplied by the height. And this is where the height is the perpendicular height, so it’s perpendicular to the base. So therefore, for shape 1, it’s gonna be a half multiplied by 27 multiplied by 18, which is gonna give an area of 243 centimeters squared.

Okay, great. So now, let’s move on to shape 2. Once again, we’ve got a triangle for shape 2. But this time, I’ve marked on our vertices as well, just so we can see them. It’s 𝐵𝐷𝐸. And we can see that our base is 50.4 because that’s 𝐷𝐸. And our height is going to be 36. And that’s because we’ve got 𝐴𝐵 and 𝐴𝐷, both 18. Add these together, and this gives us 36. So once again, we use the formula for the area of a triangle. So we’ve got that the area is equal to a half multiplied by 50.4 multiplied by 36, which gives an area of 907.2 centimeters squared. Okay, great. So that’s shape 1 and shape 2.

So now, let’s move on to shape 3. Then for shape 3, again, it’s a triangle. And this time, we’ve got a triangle 𝐴𝐶𝐻. And we can see that the top base is 27. And then if we want to find the height, this is gonna be 72. And that’s cause we’ve got 𝐴𝐷 which is 18 add 𝐷𝐺 which is 27 add 𝐺𝐻 which is also 27. So then, once again, using the same formula for the area of a triangle, we’ve got a half multiplied by 27 multiplied by 72 which is gonna give an area of shape 3 of 972 centimeters squared.

Okay, great. Let’s move on to shape 4. Well, shape 4 is a trapezoid. And what we’ve got is a trapezoid 𝐷𝐸𝐺𝐹. And we can see here that we’ve got a formula for the area of a trapezoid. And that is that we have a half multiplied by 𝑎 plus 𝑏 multiplied by ℎ, where 𝑎 and 𝑏 are the parallel sides and ℎ is the height or distance between them. So we can see, in our shape, we’ve got our 𝑎 and 𝑏 as 50.4 and 36. And then our ℎ is gonna be 27. So the area of shape 4 is gonna be equal to a half multiplied by, then we’ve got 50.4 add 36 multiplied by 27 which is gonna give us an area for shape 4 of 1166.4 centimeters squared.

And then finally, for shape 5, we’ve got another triangle. So what we’re gonna do is we’re gonna have a half multiplied by, then our base here of 36, then multiplied by the height of 27, which is gonna give us an area for the fifth shape of 486 centimeters squared. So okay, great. We’ve now worked out the area of each of our smaller shapes. So now, what we need to do is put these all together to give us our area of our total shape 𝐵𝐸𝐹𝐻𝐶.

So therefore, we can say that the area of the shape 𝐵𝐸𝐹𝐻𝐶 is gonna be equal to 243 add 907.2 add 972 add 1166.4 add 486. So therefore, that’s gonna give us 3774.60 centimeters squared. Well, when we put that into our calculator, we get 3774.6 centimeters squared. But if you check the question, it asks us to have the answer to the nearest hundredth. So I’ve added the zero. So that’s our final answer.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.