The bases of the trapezoid are 6 dm and 2 dm, the sides are 0.13 m and 0.37 m. Find the area of the trapezoid.

The area of ​​a trapezoid can be found, knowing the lengths of all its sides, by the formula:

S = (a + b) / 2 * √ (c² – 1/4 * ((c² – d²) / (b – a) + b – a) ²),

where a is the smaller base, b is the larger base, c and d are the sides.

1. Let’s translate 6 dm and 2 dm in centimeters.

1 dm = 10 cm, then:

6 dm = 6 * 10 cm = 60 cm;

2 dm = 2 * 10 cm = 20 cm.

2. Let’s translate 0.13 m and 0.37 m in centimeters.

1 m = 100 cm, then:

0.13 m = 0.13 * 100 cm = 13 cm;

0.37 m = 0.37 * 100 cm = 37 cm.

3. Thus, the bases of the trapezoid are 60 cm and 20 cm, and the sides are 13 cm and 37 cm.

Substitute these values ​​into the area formula:

S = (20 + 60) / 2 * √ (13² – 1/4 * ((13² – 37²) / (60 – 20) + 60 – 20) ²) = 80/2 * √ (169 – 1/4 * ((169 – 1369) / 40 + 40) ²) = 40 * √ (169 – 1/4 * (- 1200/40 + 40) ²) = 40 * √ (169 – 1/4 * (- 30 + 40 ) ²) = 40 * √ (169 – 1/4 * 10²) = 40 * √ (169 – 1/4 * 100) = 40 * √ (169 – (1 * 100) / 4) = 40 * √ (169 – 100/4) = 40 * √ (169 – 25) = 40 * √144 = 40 * 12 = 480 (cm²).

Answer: S = 480 cm².