The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper WYZB that measures 21 cm by 13 cm. WX = AZ = 5 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 80°. Find ∠XAZ in Figure 2.
(a)
Area of Rectangle WYZB
= 21 x 13
= 273
Area of Triangle WXB
=
12 x 5 x 13
= 32.5 cm
2 Area of Triangle XBA
= (273 - 32.5 - 32.5) ÷ 2
= 208 ÷ 2
= 104 cm
2 Area of WXAZB
= 104 + 32.5 + 32.5
= 169 cm
2 (b)
∠BXA
= (180° - 80°) ÷ 2
= 100 ÷ 2
= 50° (Angles on a straight line)
∠XAZ
= 360° - 90° - 90° - 50°
= 130° (Sum of angles in a quadrilateral)
Answer(s): (a) 169 cm
2; (b) 130°