please help i got this asignment and i cant find the way to solve it

[lost peak]

The blue area is the cross-section (what you see when you cut the profile perpendicular to its length).

The total width of the profile is 46 mm.

The height from the base to the top curve is 6.5 mm.

Both bottom corners are angled at 20°, forming triangular ends.

The top edge is curved, forming part of a circle with a radius of 100 mm.

The task is to calculate the area of the blue cross-section by breaking it into parts:

The two triangular corners (each formed by the 6.5 mm height and a 20° angle)

The middle part with a curved top (a circular arc of radius 100 mm)

[lost peak]

ps the ansewer in tho book says its 312mm2

[brittle vault]

Im working on this

[brittle vault]

I have not found the entire process, but I believe I have made a step. The big piece of missing information is the angle theta of the sector that has been cut out of the piece, and I believe that this is found via a simultaneous solution using chords.

If we look at the chord from points A, B (being the top corner/edge/pointy things on this shape) then there is some theta for chord AB given R=100 proportional to the chord = 46mm of radius 100+z, and matching theta for them both

Setting up this relationship, recall chord = 2r*sin(theta/2), gives:

46 = 2(100+z)*sin(theta / 2)
AB = 2(100)*sin(theta / 2)

Note that theta is not 40 deg, which you would get from solving the triangle with angles 70/70 from the slant. This is because the centre of the circle R=100 is not at the top of that triangle. If you solve it like that, you get that AB equals 68.4mm. This cannot possibly be the case because we know that AB < 46mm.

Additionally, there is a (probably not so useful) upper-bound on theta, theta_upper = 26.60. This comes from solving the chord equation for 46=2(100)*sin(theta/2), which is the chord of circle R=100 to get chord=46. This is derived from the idea that AB < 46 as outlined above.