PSLE In Figure 1, NPQR 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 60 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle NPQR
= 34 x 18
= 612 cm
2 Area of the 6 triangles
= 612 - 486
= 126 cm
2 Area of each triangle that was cut out
= 126 ÷ 6
= 21 cm
2 (b)
Perimeter of Rectangle NPQR
= 2(34 + 18)
= 2 x 52
= 104 cm
Perimeter of Figure 2
= 104 + 60
= 164 cm
Sum of the lengths of all the jagged edges
= 164 - (2 x 34)
= 164 - 68
= 96 cm
Sum of the lengths of the jagged edges of 1 triangle
= 96 ÷ 6
= 16 cm
Base of each triangle
= 18 ÷ 3
= 6 cm
Perimeter of each triangle
= 16 + 6
= 22 cm
Answer(s): (a) 21 cm
2; (b) 22 cm