PSLE In Figure 1, ABCD 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 756 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 104 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle ABCD
= 36 x 28
= 1008 cm
2 Area of the 8 triangles
= 1008 - 756
= 252 cm
2 Area of each triangle that was cut out
= 252 ÷ 8
= 31.5 cm
2 (b)
Perimeter of Rectangle ABCD
= 2(36 + 28)
= 2 x 64
= 128 cm
Perimeter of Figure 2
= 128 + 104
= 232 cm
Sum of the lengths of all the jagged edges
= 232 - (2 x 36)
= 232 - 72
= 160 cm
Sum of the lengths of the jagged edges of 1 triangle
= 160 ÷ 8
= 20 cm
Base of each triangle
= 28 ÷ 4
= 7 cm
Perimeter of each triangle
= 20 + 7
= 27 cm
Answer(s): (a) 31.5 cm
2; (b) 27 cm