Find the length of the stock needed to create the shape as shown the right. A stock with a thickness of 4 centimeters can be divided into three parts from left to right: a vertical part of length 20 centimeters; a curved surface extending outwards that is one-quarter of a full circle of radius 8 centimeters; horizontal part of length 25 centimeters. The length of the stock needed to create the shape is approximately nothing ▼ cm squared . cm. (Simplify your answer. Round to the nearest tenth as needed.)

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step-by-step explanation:

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look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3