September 2, 2021
Original: Useful Geometry Formulas (2509)
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Title: Useful geometry formulas
There are four shapes, with formulas below each.
The first shape is just a circle, with the radius labeled r. The formula is A = πr2.
The second shape is an up-pointing triangle with half an ellipse below it, with the triangle and ellipse sharing a side. The outline of the entire shape looks like a 2D representation of a cone, but the dividing lines inside don't suggest it's a cone. Rather, the bottom of the triangle is drawn (as a horizontal line), and there's a vertical dashed line dividing the triangle down the center. The height of the triangle is labeled h, half of the triangle's base (and one radius of the half-ellipse) is labeled b, and the other radius of the half-ellipse is labeled a. The formula is "A = 1/2 πab + bh".
The third shape is a rectangle with two half-ellipses stuck to the top and bottom. The outline of the whole shape looks like a 2D representation of a cylindar, but the internal lines show the edges of the rectangle, making it not look as much like a cylendar. The width of the rectangle (and one diameter of the two half-ellipses) is labeled d, the height of the rectangle is labeled h, and the other radius of the half-ellipses is labeled r. The formula is "A = d(πr/2 + h)".
The fourth shape looks like a 2D representation of a 3D box, made out of a rectangle and two parallelograms. The rectangle is h by b, the other side of one of the parallelograms is d, and the angle of that parallelogram is θ. There are also dotted lines showing part of the parallelogram as a right triangle. The formula is "A = bh + d(b sin θ + h cos θ)".
Title text: It's often helpful to break problems down into smaller parts