PSLE In Figure 1, PQRS is a rectangular piece of paper. After 8 identical triangles are cut out from the paper, the remaining paper is shown in Figure 2. The area of the remaining paper is 924 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 72 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle PQRS
= 38 x 28
= 1064 cm
2 Area of the 8 triangles
= 1064 - 924
= 140 cm
2 Area of each triangle that was cut out
= 140 ÷ 8
= 17.5 cm
2 (b)
Perimeter of Rectangle PQRS
= 2(38 + 28)
= 2 x 66
= 132 cm
Perimeter of Figure 2
= 132 + 72
= 204 cm
Sum of the lengths of all the jagged edges
= 204 - (2 x 38)
= 204 - 76
= 128 cm
Sum of the lengths of the jagged edges of 1 triangle
= 128 ÷ 8
= 16 cm
Base of each triangle
= 28 ÷ 4
= 7 cm
Perimeter of each triangle
= 16 + 7
= 23 cm
Answer(s): (a) 17.5 cm
2; (b) 23 cm