PSLE In Figure 1, PQRS is a rectangular piece of paper. After 4 identical triangles are cut out from the paper, the remaining paper is shown in Figure 2. The area of the remaining paper is 348 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 32 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle PQRS
= 34 x 12
= 408 cm
2 Area of the 4 triangles
= 408 - 348
= 60 cm
2 Area of each triangle that was cut out
= 60 ÷ 4
= 15 cm
2 (b)
Perimeter of Rectangle PQRS
= 2(34 + 12)
= 2 x 46
= 92 cm
Perimeter of Figure 2
= 92 + 32
= 124 cm
Sum of the lengths of all the jagged edges
= 124 - (2 x 34)
= 124 - 68
= 56 cm
Sum of the lengths of the jagged edges of 1 triangle
= 56 ÷ 4
= 14 cm
Base of each triangle
= 12 ÷ 2
= 6 cm
Perimeter of each triangle
= 14 + 6
= 20 cm
Answer(s): (a) 15 cm
2; (b) 20 cm