Solve these 10 parallelograms practice problems, exercises and tests. For each problem, you can apply the relevant formula or concept from: Parallelogram Formulas and Calculation Examples. You may want to use a calculator for calculations involving square roots, trigonometric functions, and vector operations.
Study Parallelogram Formulas and Calculation Examples.
Area Calculation: Find the area of a parallelogram with a base of 8 inches and a height of 5 inches.
Perimeter Calculation: Calculate the perimeter of a parallelogram with a base of 10 feet and an adjacent side of 7 feet.
Diagonal Lengths: Given a parallelogram with a base of 6 inches and a height of 4 inches, calculate the lengths of its diagonals using the Pythagorean theorem.
Interior Angles: If one of the opposite angles in a parallelogram measures 60 degrees, what are the measures of the interior angles?
Height Calculation: Determine the height of a parallelogram with an area of 72 square inches and a base length of 8 inches.
Diagonal Length using Law of Cosines: Calculate the length of the diagonal "x" in a parallelogram with side lengths a = 9 feet, b = 12 feet, and the included angle A = 120 degrees.
Area Calculation using Vectors: Given two vectors a = (3, 2) and b = (5, 1), find the area of the parallelogram they form.
Sides from Diagonals and Angle: In a parallelogram with diagonals d1 = 10 inches and d2 = 8 inches, and an angle γ = 45 degrees between them, calculate the lengths of sides a and b.
Sides from Diagonals and Known Side: If you have a parallelogram with diagonals d1 = 6 feet and d2 = 8 feet and a known side "a" of 4 feet, find the length of side "b."
Sides from Altitude and Angle: In a parallelogram, if the altitude (height) is 10 inches and one of the angles α = 30 degrees, calculate the lengths of sides a and b.
