Area of Quadrilateral

A quadrilateral is a polygon that has 4 sides. You can use formulas to find the area of quadrilaterals.

Figure Area Formula

Rectangle

Square

A=lw, where l represents the length and w represents the height. Or A=bh, where b represents the base length and h represents the height.

A=s2, where s represents the length of a side.

Example 1: What is the area of this rectangle?

Strategy: Use the formula for the area of a rectangle.Step 1: Substitute the values for the length and width into the formula.

-The length of the rectangle is 7 feet and the width is 5 feet.

A= l∙w A= 7∙5

Step 2: Multiply A= 7∙5 = 35

Solution: The area of the rectangle is 35 square feet, or 35 ft2.

5 ft

7 ft

Figure Area Formula

Parallelogram A=bh, where b represents the base length and h represents the height.

Example 2: What is the area of this parallelogram?

Strategy: Use the formula for the area of a parallelogram.Step 1: Substitute the values for the base and height into the formula.

-The base of the parallelogram is 15 cm and the height is 6 cm.

A= b∙h A= 15∙6

Step 2: Multiply A= 15∙6 = 90

Solution: The area of the parallelogram is 90 square

centimeters, or 90 cm2.

6 cm7.5 cm

15 cm

Figure Area Formula

Rhombus A=bh, where b represents the base length and h represents the height.

Example 3: What is the area of this rhombus?

Strategy: Use the formula for the area of a rhombus.Step 1: Substitute the values for the base and height into the formula.

-The base of the rhombus is 13 in and the height is 12 in. A= b∙h A= 13∙12

Step 2: Multiply A= 13∙12 = 156

Solution: The area of the rhombus is 156 square inches, or 156 in2.

13 in

12in A rhombus is a parallelogram whose sides are all the same length.

Figure Area Formula

Trapezoid A=1/ 2 h(a+b), where h represents the height and a and b represent the lengths of the bases.

Example 4: What is the area of this trapezoid?

Strategy: Use the formula for the area of a trapezoid.Step 1: Substitute the values for the base and height into the formula.

-The height of the trapezoid is 7 yards and the bases are 8 yards and 14 yards. A= 1/2 h(a+b) A= 1/2 ∙7(8+14)

Step 2: Use the order of operations. (PEMDAS) -1st Parentheses A= 1/2 ∙7(22) -2nd Multiply A= 1/2 ∙154 = ∙ = = 77

Solution: The area of the trapezoid is 77 square yards, or 77 yd2.

7 yd

14 yd

8 yd