High-School-Kid said:
Well it's 120 mm from the base to the top
Ah. So it's not the
sides that have a length of 120 millimeters, but the
height. That's quite a bit different. :shock:
Draw the triangle with the pointy corners, and draw a circle inside the peak angle. Draw a radius line from the center of the circle to where the circle meets the triangle. This radius line, by nature, is perpendicular to the side of the triangle.
Draw the altitude line of the triangle, thus splitting the triangle into two 30-60-90 triangles. Note that you now have a right triangle formed by (half of) the peak angle of the original triangle, the corner at the circle's center, and the point where the radius line meets the triangle. Use what you know about 30-60-90 triangles, along with the known value of the circle's radius, to find the length of the segment between the peak of the original angle and the center of the circle.
Since the total height of the rounded-triangle figure is 120, and since the radius of the circle is 10, then what is the height, above the base of the rounded-triangle figure, of the circle's center? Now that you have the length of the segment between the circle's center and the peak of the "regular" triangle, what is the height of the regular triangle?
Using what you know about 30-60-90 triangles, what then must be the length of the base of the regular triangle?
Now that you have the height and base of the regular triangle, find the total area.
Comparing the regular triangle with the rounded one, the area of the rounded triangle will be the area of the regular triangle, less the areas of the three corners (the triangles with bases parallel to the opposite side of the triangle and passing through their circles' centers), plus half the areas of the corners' circles.
See what you can do with this. If you get stuck, please reply showing how far you have gotten.
Thank you!
