A cross-section of an irrigation canal has the shape of an isosceles trapezoid. The flat bottom of the canal is meters wide, the open water surface at the top is meters wide, and the vertical depth of the canal is meters. To prevent seepage, a waterproof lining is applied only to the flat bottom and the two slanted sides of the canal. What is the total length, in meters, of the canal's cross-section that receives this lining?
Cevap: 36 meters
Cevap
36
The lined portion consists of the flat bottom and the two slanted sides. By dropping perpendicular altitude lines from the top corners to the bottom plane, two identical right triangles are formed on the left and right edges. The horizontal base of each right triangle is half of the difference between the top and bottom widths: meters. The vertical height of the canal is given as meters. Using the Pythagorean theorem (), the length of each slanted side is meters. The total length of the waterproof lining is the sum of the bottom width and the two slanted sides: meters.
Adım Adım Çözüm
Anahtar Kavram
Calculating the partial perimeter of a composite/trapezoidal figure using the Pythagorean theorem.