PSLE In Figure 1, ABCD is a rectangular piece of paper. After 6 identical triangles are cut out from the paper, the remaining paper is shown in Figure 2. The area of the remaining paper is 486 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 48 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle ABCD
= 36 x 18
= 648 cm
2 Area of the 6 triangles
= 648 - 486
= 162 cm
2 Area of each triangle that was cut out
= 162 ÷ 6
= 27 cm
2 (b)
Perimeter of Rectangle ABCD
= 2(36 + 18)
= 2 x 54
= 108 cm
Perimeter of Figure 2
= 108 + 48
= 156 cm
Sum of the lengths of all the jagged edges
= 156 - (2 x 36)
= 156 - 72
= 84 cm
Sum of the lengths of the jagged edges of 1 triangle
= 84 ÷ 6
= 14 cm
Base of each triangle
= 18 ÷ 3
= 6 cm
Perimeter of each triangle
= 14 + 6
= 20 cm
Answer(s): (a) 27 cm
2; (b) 20 cm