Calculations at a rectangle with one vertex cut off. This is a convex pentagon with three adjacent right angles. The cut off vertex has the shape of a right triangle with legs of length a-c and b-d and a hypotenuse of length e.
Enter the lengths of the four straight sides and choose the number of decimal places. Then click Calculate.
Formulas:
e = √ (a-c)² + (b-d)²
p = a + b + c + d + e
A = a * b - ( a - c ) * ( b - d ) / 2
Lengths and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
The two corners created by cutting off a right-angled corner are obtuse angles, meaning they have between 90 and 180 degrees, but not exactly one of these values. These two angles add up to 270 degrees, the same as the other three angles combined, which are right angles. The slanted side created by cutting off the corners can be shorter, equal to, or longer than any of the other four sides. If the cut corner passes through an existing corner, the result is not a pentagon, but a right trapezoid. If the cut passes through two opposite corners, the rectangle is bisected diagonally, creating two equal right triangles with the diagonal of the original rectangle as the hypotenuse.
Calculating this figure is quite simple. The length of the slanted side is calculated using the Pythagorean theorem with the two missing pieces a-c and b-d as the legs. The area of the cut rectangle is the area of the original rectangle minus the area of the cut-off right triangle. Finally, the perimeter is simply the lengths of all five sides added together. The lengths of the three different diagonals can be calculated using the Pythagorean theorem; these are the hypotenuses in the corresponding right triangle with a, b, or b, c, or a, d as the legs.