The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper PRSU that measures 18 cm by 16 cm. PQ = TS = 6 cm. The paper is folded along the dotted line QT such that point R touches point U, as shown in Figure 2.
- Find the area of Figure 2. PQTSU, after the folding.
- In Figure 2, ∠PQU is 74°. Find ∠QTS in Figure 2.
(a)
Area of Rectangle PRSU
= 18 x 16
= 288
Area of Triangle PQU
=
12 x 6 x 16
= 48 cm
2 Area of Triangle QUT
= (288 - 48 - 48) ÷ 2
= 192 ÷ 2
= 96 cm
2 Area of PQTSU
= 96 + 48 + 48
= 192 cm
2 (b)
∠UQT
= (180° - 74°) ÷ 2
= 106 ÷ 2
= 53° (Angles on a straight line)
∠QTS
= 360° - 90° - 90° - 53°
= 127° (Sum of angles in a quadrilateral)
Answer(s): (a) 192 cm
2; (b) 127°