PSLE In Figure 1, QRST 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 QRST
= 30 x 15
= 450 cm
2 Area of the 6 triangles
= 450 - 360
= 90 cm
2 Area of each triangle that was cut out
= 90 ÷ 6
= 15 cm
2 (b)
Perimeter of Rectangle QRST
= 2(30 + 15)
= 2 x 45
= 90 cm
Perimeter of Figure 2
= 90 + 54
= 144 cm
Sum of the lengths of all the jagged edges
= 144 - (2 x 30)
= 144 - 60
= 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) 15 cm
2; (b) 19 cm