PSLE In Figure 1, STUV 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 992 cm
2.
- What is the area of each triangle that was cut out?
- The perimeter of Figure 2 is 96 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle?
(a)
Area of Rectangle STUV
= 39 x 32
= 1248 cm
2 Area of the 8 triangles
= 1248 - 992
= 256 cm
2 Area of each triangle that was cut out
= 256 ÷ 8
= 32 cm
2 (b)
Perimeter of Rectangle STUV
= 2(39 + 32)
= 2 x 71
= 142 cm
Perimeter of Figure 2
= 142 + 96
= 238 cm
Sum of the lengths of all the jagged edges
= 238 - (2 x 39)
= 238 - 78
= 160 cm
Sum of the lengths of the jagged edges of 1 triangle
= 160 ÷ 8
= 20 cm
Base of each triangle
= 32 ÷ 4
= 8 cm
Perimeter of each triangle
= 20 + 8
= 28 cm
Answer(s): (a) 32 cm
2; (b) 28 cm