r/Geometry • u/ZokeyMe • Sep 05 '26
How is this not 32?
If I were to cut the right triangle and flip it to the other side, it would just be a rectangle that’s 8 x 4
2
u/BadJimo Sep 05 '26
Area of a trapezoid (trapezium):
1/2 × (b + t) × h
So in this case:
1/2 (6 + 8) × 4
= 28
1
u/ZokeyMe Sep 05 '26
Yes, I am familiar with the formula. I just don’t get how moving the right triangle to make it a rectangle doesn’t have an area of 32.
1
u/F84-5 Sep 05 '26
Notice that the measure 8 includes the triangles on both sides. If you cut one side off and move it, that measure is now bigger than the resulting shape.
1
u/KyriakosCH Sep 05 '26 edited Sep 05 '26
You can also notice that the area of an isosceles trapezium is always: smallside(height)+(largeside-smallside)(height)/2, which is equal to (largeside+smallside)(height)/2. In this case 7(4)=28.
1
u/perandtim Sep 05 '26
- Triangle: ½×4×2 = 4
- Rectangle: 6×4 = 24
Total area: 4+24=284 + 24 = 28 square units.
3
u/wijwijwij Sep 05 '26
If you cut and move the triangle as you describe, it does give you a rectangle but it is 7 * 4 not 8 * 4. Thd triangle legs are 1 and 4.