Questions: Geometry, Measurement, Data Analysis Perimeter of a piecewise rectangular figure Find the perimeter of the figure below. Notice that one side length is not given. Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer.

Solution Steps

The figure can be divided into two rectangles. The top rectangle has a length of 12 yd and the bottom rectangle has a length of 5 yd. The total length is 12 yd + 5 yd = 17 yd. The vertical side on the left has a length of 15 yd. The vertical side on the right is composed of two segments with lengths 11 yd and 7 yd. The sum is 11 yd + 7 yd = 18 yd. The missing side length is the difference between the total vertical length on the right (18 yd) and the total vertical length on the left (15 yd). Therefore, the missing side length is 18 yd - 15 yd = 3 yd.

The perimeter is the sum of all the side lengths. Starting from the top left and moving clockwise, the side lengths are 12 yd, 3 yd, 7 yd, 5 yd, 15 yd, and 12 yd - 7 yd = 5 yd. Since 12 yd - 7 yd = 5yd. The perimeter is 12 yd + 3 yd + 7 yd + 5 yd + 15 yd + 5 yd = 47 yd.

Final Answer