Area of trapezoid

**Lesson 1: **A trapezoid has an area of 110 square meters^{2}, the difference between the lengths of the two bases is 6m. Calculate the length of each base, knowing that if the great base is increased by 3m, the area of the trapezoid will increase by 15m^{2}.

**Solution**

The height of the given trapezoid is

\(\frac{{2×15}}{3} = 10\,\,(m)\)

The sum of the two bases of a trapezoid is

\(\frac{{2×110}}{{10}} = 22\,\,(m)\)

The length of the great bottom is

(22 + 6) : 2 = 14 (m)

The length of the small bottom is

22 – 14 = 8 (m)

**Lesson 2:** A trapezoidal field has the average length of the two bases 35.75m. If the bottom is increased by 7.2m, the area of the field will increase by 86.4m .^{2}. How many kilograms of rice did that field yield? Assume that on average each a harvests 65kg of rice.

**Solution**

The height of the trapezoidal field is

(86.4 x 2) : 7.2 = 24 (m)

The area of a trapezoidal field is

35.75 x 24 = 858 (m^{2}) or 8.58a

The number of paddy harvested in that field is

65 x 8.58 = 557.7 (kg)

**Lesson 3:** A trapezoid has a small base equal to \(\frac{3}{5}\) m, the larger base is 4 times the smaller bottom, and the height is 2.5 times the smaller bottom. Calculate the area of a trapezoid.

**Solution**

Big bottom length

\(\frac{3}{5}\,\,.\,\,4\, = \frac{{12}}{5}\,\,(m)\)

Height length

\(\frac{3}{5}\,\,.\,\,2,5\,\, = \,\frac{3}{5}\,\,.\,\,\frac{5 }{2} = \frac{3}{2}\) (m)

The area of the trapezoid is

\(\frac{{\left( {\frac{3}{5} + \frac{{12}}{5}} \right).\frac{3}{2}}}{2} = \frac {9}{4} = 2\frac{1}{4} = 2.25\,\,({m^2})\)

**Lesson 4:** Construct two altitudes of a trapezoid to form a square with two bases of perimeter 24m. Two triangles are created with bases of 2m and 3m. Calculate the area of a trapezoid.

**Solution**

Knowing the square’s perimeter is 24m, we infer that the small base side is 6m and the height is 6m.

Therefore, the major base edge is

2 + 6 + 3 = 11 (m)

The area of the trapezoid is

\(\frac{{(6 + 11.6}}{2} = 51\,\,({m^2})\)

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