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 812 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 88 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle ABCD
= 37 x 28
= 1036 cm
2 Area of the 8 triangles
= 1036 - 812
= 224 cm
2 Area of each triangle that was cut out
= 224 ÷ 8
= 28 cm
2 (b)
Perimeter of Rectangle ABCD
= 2(37 + 28)
= 2 x 65
= 130 cm
Perimeter of Figure 2
= 130 + 88
= 218 cm
Sum of the lengths of all the jagged edges
= 218 - (2 x 37)
= 218 - 74
= 144 cm
Sum of the lengths of the jagged edges of 1 triangle
= 144 ÷ 8
= 18 cm
Base of each triangle
= 28 ÷ 4
= 7 cm
Perimeter of each triangle
= 18 + 7
= 25 cm
Answer(s): (a) 28 cm
2; (b) 25 cm