The area of a polygon is the number of square units inside that polygon. Area is 2-dimensional like a carpet or an area rug.
trapezoidA trapezoid is a 4-sided figure with one pair of parallel sides. For example, in the diagram to the right, the bases are parallel. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula for the area of a trapezoid is:
area_trapezoid1.gif or area_trapezoid2.gif
Where b1.gif is base1.gif, b2.gif is base2.gif, h.gif is height and · means multiply.
Each base of a trapezoid must be perpendicular to the height. In the diagram above, both bases are sides of the trapezoid. However, since the lateral sides are not perpendicular to either of the bases, a dotted line is drawn to represent the height.
In Examples 1 and 3 below, the height is a side of the trapezoid since it is perpendicular to the base. In Example 2, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height.
Example 1: Find the area of a trapezoid with bases of 10 inches and 14 inches, and a height of 5 inches.
trapezoidSolution:
area_trapezoid2.gif
a_0.gif = one_half.gif · (10 in + 14 in) · 5 in
a_0.gif = one_half.gif · (24 in) · (5 in)
a_0.gif = one_half.gif · 120 in2
a_0.gif = 60 in2
Example 2: Find the area of a trapezoid with bases of 9 centimeters and 7 centimeters, and a height of 3 centimeters.
Solution:
trapezoidarea_trapezoid2.gif
a_0.gif = one_half.gif · (9 cm + 7 cm) · 3 cm
a_0.gif = one_half.gif · (16 cm) · (3 cm)
a_0.gif = one_half.gif · 48 cm2
a_0.gif = 24 cm2
Example 3: The area of a trapezoid is 52 square inches and the bases are 11 inches and 15 inches. Find the height.
trapezoidSolution:
area_trapezoid2.gif
52 in2 = one_half.gif· (11 in + 15 in) · h.gif
52 in2 = one_half.gif· (26 in) · h.gif
52 in2 = (13 in) · h.gif
52 in2 ÷ (13 in) = h.gif
h.gif = 4 in
trapezoidSummary: To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula for the area of a trapezoid is:
area_trapezoid1.gif or area_trapezoid2.gif
Where b1.gif is base1.gif, b2.gif is base2.gif, h.gif is height.
Step-by-step explanation:
