A clear and step-by-step explanation on how to find the area of different types of quadrilaterals, designed for 13-year-old learners.
What is a Quadrilateral?
A quadrilateral is a four-sided polygon. Examples include squares, rectangles, parallelograms, trapezoids, and rhombuses.
How to Find the Area of Quadrilaterals?
The area of a quadrilateral depends on the specific type of quadrilateral because their shapes and formulas are different. Let's go over the most common types:
A rectangle has opposite sides equal and all angles are right angles.
Formula: Area = length × width
Example: If length = 8 cm and width = 5 cm, then area = 8 × 5 = 40 cm².
A square has four equal sides and all right angles.
Formula: Area = side × side = side²
Example: Side = 6 cm, area = 6 × 6 = 36 cm².
A parallelogram has opposite sides equal and opposite angles equal. The height is the perpendicular distance between the bases.
Formula: Area = base × height
Example: Base = 10 cm, height = 4 cm, area = 10 × 4 = 40 cm².
A trapezoid has only one pair of parallel sides. The two parallel sides are called bases.
Formula: Area = 1/2 × (sum of parallel sides) × height
Example: If the two bases are 8 cm and 5 cm, and the height is 4 cm, then area = 1/2 × (8 + 5) × 4 = 1/2 × 13 × 4 = 26 cm².
A rhombus has four equal sides, and opposite angles are equal. You can find its area using either base × height or using its diagonals.
Formula using base and height: Area = base × height
Formula using diagonals: Area = 1/2 × (diagonal 1) × (diagonal 2)
Example using diagonals: If the diagonals are 10 cm and 6 cm, area = 1/2 × 10 × 6 = 30 cm².
Remember, knowing the shape and its properties helps you pick the right formula. Practice by drawing each shape and try calculating areas with different numbers.