The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper PRSU that measures 22 cm by 15 cm. PQ = TS = 4 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 77°. Find ∠QTS in Figure 2.
(a)
Area of Rectangle PRSU
= 22 x 15
= 330
Area of Triangle PQU
=
12 x 4 x 15
= 30 cm
2 Area of Triangle QUT
= (330 - 30 - 30) ÷ 2
= 270 ÷ 2
= 135 cm
2 Area of PQTSU
= 135 + 30 + 30
= 195 cm
2 (b)
∠UQT
= (180° - 77°) ÷ 2
= 103 ÷ 2
= 51.5° (Angles on a straight line)
∠QTS
= 360° - 90° - 90° - 51.5°
= 128.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 195 cm
2; (b) 128.5°