PSLE In Figure 1, QRST 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 420 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 56 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle QRST
= 26 x 20
= 520 cm
2 Area of the 8 triangles
= 520 - 420
= 100 cm
2 Area of each triangle that was cut out
= 100 ÷ 8
= 12.5 cm
2 (b)
Perimeter of Rectangle QRST
= 2(26 + 20)
= 2 x 46
= 92 cm
Perimeter of Figure 2
= 92 + 56
= 148 cm
Sum of the lengths of all the jagged edges
= 148 - (2 x 26)
= 148 - 52
= 96 cm
Sum of the lengths of the jagged edges of 1 triangle
= 96 ÷ 8
= 12 cm
Base of each triangle
= 20 ÷ 4
= 5 cm
Perimeter of each triangle
= 12 + 5
= 17 cm
Answer(s): (a) 12.5 cm
2; (b) 17 cm