a quadrilateral is a polygon that has 4 sides. you can use formulas to find the area of...
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Area of Quadrilateral
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A quadrilateral is a polygon that has 4 sides. You can use formulas to find the area of quadrilaterals.
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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.
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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
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Figure Area Formula
Parallelogram A=bh, where b represents the base length and h represents the height.
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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
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Figure Area Formula
Rhombus A=bh, where b represents the base length and h represents the height.
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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.
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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.
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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