The figure below is a figure overlapping three rectangular papers with 3cm in length and 15cm in width.
The area of the shadow is 102 cm2.
Find the total length of bold lines.
Answer
64 cm
Solution
The area of one rectangle is 3 × 15 = 45cm2.
Because there are three sheets, it is 45 × 3 = 135cm2 in total.
The difference with the shadow area is 135 - 102 = 33cm2.
This difference is the area of the part that rectangles overlapping.
The total length of one side of three lozenges is 33/3 = 11cm.
The total length of perimeter of three rectangles is (3 + 15 ) × 2 × 3 = 108cm.
The total length of perimeter of three lozenges is 11 × 4 = 44cm.
Therefore, the total length of the bold lines is 108 - 44 = 64cm.
