How to Find the Area of a Rectangle With the Length of the Diagonal & the Intersection Angle

A rectangle is a quadrilateral with four angles equal to 90 degrees with opposite sides of this shape being parallel and equal to each other. To calculate the area of the rectangle, you need to multiply the width of the rectangle by its height. A diagonal is the line that divides the rectangle into two right triangles. The diagonal is the hypotenuse of this triangle while two other sides are width and height of the rectangle. To compute sides of the triangle, you need to use the sine and cosine of the intersection angle.

Things You'll Need

• Calculator

Instructions

1. Calculate the sine of the angle with the calculator. For example, if the angle is 30 degrees, then sin(30) = 0.5.

2. Multiply the diagonal by the sine of the angle to calculate the height of the rectangle. For example, if the diagonal is 10 inches, the height is 10 x 0.5 = 5 inches.

3. Calculate the cosine of the angle with the calculator. In this example, cos(30) = 0.866.

4. Multiply the diagonal by the cosine of the angle to calculate the width of the rectangle. In this example, the width is 10 x 0.866 = 8.66 inches.

5. Multiply the width and the height of the rectangle to calculate the area. In this example, the area of the rectangle is 8.66 x 5 = 43.3 square inches.

References

• Maths Is Fun: Area of Plane Shapes
• Math Warehouse: Rectangle -- Shape and Properties
• Clark University; Right Triangles; David E. Joyce; 1999