PSLE In Figure 1, ABCD 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 396 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 48 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle ABCD
= 29 x 18
= 522 cm
2 Area of the 6 triangles
= 522 - 396
= 126 cm
2 Area of each triangle that was cut out
= 126 ÷ 6
= 21 cm
2 (b)
Perimeter of Rectangle ABCD
= 2(29 + 18)
= 2 x 47
= 94 cm
Perimeter of Figure 2
= 94 + 48
= 142 cm
Sum of the lengths of all the jagged edges
= 142 - (2 x 29)
= 142 - 58
= 84 cm
Sum of the lengths of the jagged edges of 1 triangle
= 84 ÷ 6
= 14 cm
Base of each triangle
= 18 ÷ 3
= 6 cm
Perimeter of each triangle
= 14 + 6
= 20 cm
Answer(s): (a) 21 cm
2; (b) 20 cm