The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper WYZB that measures 18 cm by 13 cm. WX = AZ = 6 cm. The paper is folded along the dotted line XA such that point Y touches point B, as shown in Figure 2.
- Find the area of Figure 2. WXAZB, after the folding.
- In Figure 2, ∠WXB is 73°. Find ∠XAZ in Figure 2.
(a)
Area of Rectangle WYZB
= 18 x 13
= 234
Area of Triangle WXB
=
12 x 6 x 13
= 39 cm
2 Area of Triangle XBA
= (234 - 39 - 39) ÷ 2
= 156 ÷ 2
= 78 cm
2 Area of WXAZB
= 78 + 39 + 39
= 156 cm
2 (b)
∠BXA
= (180° - 73°) ÷ 2
= 107 ÷ 2
= 53.5° (Angles on a straight line)
∠XAZ
= 360° - 90° - 90° - 53.5°
= 126.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 156 cm
2; (b) 126.5°