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 928 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 ABCD
= 38 x 32
= 1216 cm
2 Area of the 8 triangles
= 1216 - 928
= 288 cm
2 Area of each triangle that was cut out
= 288 ÷ 8
= 36 cm
2 (b)
Perimeter of Rectangle ABCD
= 2(38 + 32)
= 2 x 70
= 140 cm
Perimeter of Figure 2
= 140 + 128
= 268 cm
Sum of the lengths of all the jagged edges
= 268 - (2 x 38)
= 268 - 76
= 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) 36 cm
2; (b) 32 cm