PSLE In Figure 1, DEFG 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 896 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 128 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle DEFG
= 39 x 32
= 1248 cm
2 Area of the 8 triangles
= 1248 - 896
= 352 cm
2 Area of each triangle that was cut out
= 352 ÷ 8
= 44 cm
2 (b)
Perimeter of Rectangle DEFG
= 2(39 + 32)
= 2 x 71
= 142 cm
Perimeter of Figure 2
= 142 + 128
= 270 cm
Sum of the lengths of all the jagged edges
= 270 - (2 x 39)
= 270 - 78
= 192 cm
Sum of the lengths of the jagged edges of 1 triangle
= 192 ÷ 8
= 24 cm
Base of each triangle
= 32 ÷ 4
= 8 cm
Perimeter of each triangle
= 24 + 8
= 32 cm
Answer(s): (a) 44 cm
2; (b) 32 cm