**Finding the area of a trapezoid :**

The area of a trapezoid is half its height multiplied by the sum of the lengths of its two bases.

**A = (1/2) h (b₁ + b₂)**

Going through the history of ancient period and also that of medieval period, we do find the mention of statistics in many countries.

Notice that two copies of the same trapezoid fit together to form a parallelogram. The height of the parallelogram is the same as the height of the trapezoid.

The length of the base of the parallelogram is the sum of the lengths of the two bases (b₁ and b₂**)** of the trapezoid.

So, the area of a trapezoid is half the area of the parallelogram.

**Example 1 :**

A section of a deck is in the shape of a trapezoid. What is the area of this section of the

**Solution :**

here b₁ = 17 ft, b₂ = 39 ft and h = 16 ft

Area of trapezoid = (1/2) h (b₁ + b₂)

Substituting the above values in the formula, we get

= (1/2) x 16 (17 + 39)

= 8 (56) = 448 square ft

**Example 2 :**

The length of one base of a trapezoid is 27 feet, and the length of the other base is 34 feet. The height is 12 feet. What is its area?

**Solution :**

here b₁ = 27 ft, b₂ = 34 ft and h = 12 ft

Area of trapezoid = (1/2) h (b₁ + b₂)

Substituting the above values in the formula, we get

= (1/2) x 12 (34 + 27)

= 6 (61) = 366 square ft

**Example 3 :**

Simon says that to find the area of a trapezoid, you can multiply the height by the top base and the height by the bottom base. Then add the two products together and divide the sum by 2. Is Simon correct? Explain your answer.

**Solution :**

Yes;

Simon uses the Distributive Property to multiply each base by the height. Then he finds the sum BY multiplying by 1/2 is the same as dividing by 2

**Example 4 :**

The height of a trapezoid is 8 in. and its area is 96 square inches. One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases?

**Solution :**

here, h = 8 inches

Area of the trapezoid = 96 square inches

base lengths are b₁ and b₂ respectively.

b₁ = b₂ + 6

(1/2) x 8 (b₂ + 6 + b₂) = 96

4 (2b₂ + 6) = 96

2b₂ + 6 = 24

2b₂ = 18

b₂ = 9

By applying the value of b₂ in the equation b₁ = b₂ + 6, we get

b₁ = 9 + 6 ==> b₁ = 15 inches

Hence, base lengths are 9 inches and 15 inches

- Area and polygons
- Inverse operations
- Area of square and rectangles
- Area of quadrilaterals
- Area of a parallelogram
- Finding the area of a trapezoid
- Finding the area of a rhombus
- Area of triangles
- Finding the area of a triangle
- Problems using area of a triangles
- Solving area equations
- Writing equations using the area of a trapezoid
- Solving multistep problems
- Area of polygons
- Finding areas of polygons
- Real world problems involving area and perimeter of polygon

After having gone through the stuff given above, we hope that the students would have understood "Finding the area of a trapezoid".

Apart from the stuff given above, if you want to know more about "Finding the area of a trapezoid", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**