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Home > CCG > Chapter 6 > Lesson 6.2.1 > Problem 6-57

6-57.

The shaded figures below are similar.

An irregular quadrilateral enclosed by a rectangle. The 2 shapes share the left base, 22 centimeters. Outside the shaded irregular quadrilateral are 2 right triangles, one at the top right corner with a leg, 24, also the length of the rectangle, & another leg, 10, down the right side of the rectangle. The other right triangle is at the lower right corner of the rectangle with a leg, 5, going left from the bottom right rectangle corner, and another leg, 12, up the right side of the rectangle.

An irregular quadrilateral enclosed by a rectangle. The 2 shapes share the left base, m centimeters. Outside the shaded irregular quadrilateral are 2 right triangles, one at the top right corner with a leg, n, also the length of the rectangle, & another leg, 15, down the right side of the rectangle. The other right triangle is at the lower right corner of the rectangle with a leg, going left from the bottom right rectangle corner, and another leg, up the right side of the rectangle.

  1. Solve for and .

    Use the proportion  to find .

    Then write another portion for .

  2. Find the area and perimeter of each figure

    Can you use the dotted lines to make right triangles so that you can solve for the lengths of the unknown sides?

    Perimeter of smaller figure =  cm

    area of rectangle:

    area of top triangle: 

    area of bottom triangle: 

    area of shaded region =
    rectangle − top triangle − bottom triangle