Question

Find the area of this 'composite' shape:
a rectangle 8m width by 35m length, and and additional segment on top of the length wise part of the rectangle. The vertex of the segment is 15m from the base of the rectangle. The rectangle is easy, the segment is confusing

Answer 1

First of all, thanks for making and sharing this drawing, and for having done some work yourself before asking for help.

The "segment" on top the longer side of the rectangle has a vertex, and that vertex is 15 m above the base of the rectangle. We'll assume that the lower, longer side of the rectangle is on the x-axis.

Answer 2

Subtract the width of the rectangle from 15 m to obtain the height of the "segment."

I see you're assuming that the "segment" of area is rounded on top (and might even part of a circle. In contrast, I'm assuming that the "segment" is a triangle (because a triangle can have a vertex, not a circle).

Thus, knowing that the base of this triangle AND the height of the triangle, what is the area of the triangle? Add this area to the area of the rectangle, and what do you then get?

Answer 3

Hi @mathmale I appreciate your response, as I hadn't had a response for a while for this question.
The segment is actually part of a circle, I just worded my initial question wrong.
The nature of this question is that of a tunnel, which width is 35m and its walls 8m high, and a circular arch roof 15m above the centre of the road.
The height of the segment can be found by 15m-8m which is 7m, this is where I am stuck

Answer 4

Ray: we're going to need to examine our assumptions again. Is that "dome" on top the rectangle a semicircle, or only part of a semicircle? How would you know that?

Answer 5

@mathmale It's been specified to us as part of a semicircle by our teacher.
So the normal method of utilizing the area of a circle and dividing it by two will not acquire the intended result

Answer 6

that's what I was afraid of. We'll have to do some research to determine how to find the area of less than half a circle. I don't recall having done that myself at any time in the recent past. What about you? Have you a suitable reference book or reference chart that might have such a formula?

Answer 7

I had a look on the Internet and couldn't get an accurate answer. That's why I turned to the specialists (OpenStudy) ^.^
I haven't come across any.
But my view on it is to take the segment and utilize the method to find the equation of the parabola. Then I've used integration to find the area, but I don't know if it's correct