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.

AB = 0.13 m = 1.3 dm, CD = 0.37 m = 3.7 dm.

Let’s build the heights of the HВ and SK.

Quadrangle ВСKН is a rectangle, then ВН = СK, НK = ВС = 2 dm.

AH + DK = AD – НK = 6 – 2 = 4 dm.

Let AH = X cm, then DK = 4 – X cm.

In a right-angled triangle ABН, according to the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2.

In a right-angled triangle CDK, according to the Pythagorean theorem, CK ^ 2 = CD ^ 2 – DK ^ 2.

AB ^ 2 – AH ^ 2 = CD ^ 2 – DK ^ 2.

1.69 – X ^ 2 = 13.69 – 16 + 8 * X – X ^ 2.

8 * X = 4.

X = 0.5 dm.

Then BH2 = 1.69 – 0.25 = 1.44.

BH = 1.2 dm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (2 + 6) * 1.2 / 2 = 4.8 dm2.

Answer: The area of the trapezoid is 4.8 dm2.