How to measure this missing area? (replacing existing countertop)

[jessetr]

Hello!

The figure below in real life is one kitchen counter-top, all one piece. I want to replace it with something nicer, but I need to know the total area so I can get the cost of new material per square foot or inch.

Being no mathematician, my first instinct was to measure out two sections of it, but now I can't figure out the missing area (circled with a question mark). Hopefully, the measurements that are included in the picture are big enough to read. Additionally, I'm really just guessing that the obtuse angle is 35 or negative 35 degrees. Is there a way to find that angle without a protractor?

Or, is there a completely different way to measure everything to get what I need?

 

[Dr.Peterson]

Hello!

The figure below in real life is one kitchen counter-top, all one piece. I want to replace it with something nicer, but I need to know the total area so I can get the cost of new material per square foot or inch.

Being no mathematician, my first instinct was to measure out two sections of it, but now I can't figure out the missing area (circled with a question mark). Hopefully, the measurements that are included in the picture are big enough to read. Additionally, I'm really just guessing that the obtuse angle is 35 or negative 35 degrees. Is there a way to find that angle without a protractor?

Or, is there a completely different way to measure everything to get what I need?


View attachment 10153

As drawn, there is no countertop in the circled area, so there is no area to find! Did you mean to say that there is a wedge of surface between the two rectangles, either a triangle like the picture below, or maybe a sector of a circle or something else?



If so, then it would be necessary to know the angle, though a good approximation may be enough for your purposes. Or you could measure the length of the red line I drew, from which we could find the angle, or the area of the triangle.

If the angle is 35° and you want a triangle, then the area is (calling the angle C and the two sides adjacent to it a and b),

1/2 ab sin(C) = 1/2*24*24*sin(35°) = 165.2 in².

 

[sinx]

Hello!

The figure below in real life is one kitchen counter-top, all one piece. I want to replace it with something nicer, but I need to know the total area so I can get the cost of new material per square foot or inch.

Being no mathematician, my first instinct was to measure out two sections of it, but now I can't figure out the missing area (circled with a question mark). Hopefully, the measurements that are included in the picture are big enough to read. Additionally, I'm really just guessing that the obtuse angle is 35 or negative 35 degrees. Is there a way to find that angle without a protractor?

Or, is there a completely different way to measure everything to get what I need?


View attachment 10153

to figure the angle without protractor, use a framing square and find two sides of a rt triangle.
Once you know two lengths, you can calculate the angle, as ht/base=tangent of the angle (ht will be the shorter of the two sides)

you can also find the area of the triangle without knowing the angle.
measure distance between the two points, this is the base.
find the distance from the midpoint to the opposite corner. This is the ht.
Area = 1/2 base*ht.

 

[jessetr]

>>>As drawn, there is no countertop in the circled area, so there is no area to find! Did you mean to say that there is a wedge of surface between the two rectangles, either a triangle like the picture below, or maybe a sector of a circle or something else?

Yes, you're correct. There is a wedge of surface there. Your addition of that red line makes it clearer than my illustration.

View attachment 10154

>>If so, then it would be necessary to know the angle, though a good approximation may be enough for your purposes. Or you could measure the length of the red line I drew, from which we could find the angle, or the area of the triangle.

>>If the angle is 35° and you want a triangle, then the area is (calling the angle C and the two sides adjacent to it a and b),

>>1/2 ab sin(C) = 1/2*24*24*sin(35°) = 165.2 in².


So, I guess in the end I would want to know the area of two rectangles and one triangle. You know, I think I'll just bite the bullet and get a protractor to make this all easier.

This was very helpful. Thank you.

 

[jessetr]

Thank you to the two people who have responded so far.

It sounds overall like the process of finding the area of an irregular polygon. Just cut it into manageable shapes and then find the area of each piece. Then add the square inches all together.

Is that workable?

 

[mmm4444bot]

… cut it into manageable shapes and then find the area of each piece. Then add the square inches all together.

Is that workable?

Sure. Can you measure the distance shown by the red line in post #2?

If so, then you know the lengths of the triangle's three sides. There's a formula for calculating the area of a triangle, if you know all three side lengths. :cool: