PSLE In Figure 1, PQRS 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 360 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 54 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle PQRS
= 31 x 15
= 465 cm
2 Area of the 6 triangles
= 465 - 360
= 105 cm
2 Area of each triangle that was cut out
= 105 ÷ 6
= 17.5 cm
2 (b)
Perimeter of Rectangle PQRS
= 2(31 + 15)
= 2 x 46
= 92 cm
Perimeter of Figure 2
= 92 + 54
= 146 cm
Sum of the lengths of all the jagged edges
= 146 - (2 x 31)
= 146 - 62
= 84 cm
Sum of the lengths of the jagged edges of 1 triangle
= 84 ÷ 6
= 14 cm
Base of each triangle
= 15 ÷ 3
= 5 cm
Perimeter of each triangle
= 14 + 5
= 19 cm
Answer(s): (a) 17.5 cm
2; (b) 19 cm