PSLE In Figure 1, MNPQ is a rectangular piece of paper. After 4 identical triangles are cut out from the paper, the remaining paper is shown in Figure 2. The area of the remaining paper is 450 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 44 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle MNPQ
= 31 x 18
= 558 cm
2 Area of the 4 triangles
= 558 - 450
= 108 cm
2 Area of each triangle that was cut out
= 108 ÷ 4
= 27 cm
2 (b)
Perimeter of Rectangle MNPQ
= 2(31 + 18)
= 2 x 49
= 98 cm
Perimeter of Figure 2
= 98 + 44
= 142 cm
Sum of the lengths of all the jagged edges
= 142 - (2 x 31)
= 142 - 62
= 80 cm
Sum of the lengths of the jagged edges of 1 triangle
= 80 ÷ 4
= 20 cm
Base of each triangle
= 18 ÷ 2
= 9 cm
Perimeter of each triangle
= 20 + 9
= 29 cm
Answer(s): (a) 27 cm
2; (b) 29 cm