The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper XZAC that measures 22 cm by 12 cm. XY = BA = 5 cm. The paper is folded along the dotted line YB such that point Z touches point C, as shown in Figure 2.
- Find the area of Figure 2. XYBAC, after the folding.
- In Figure 2, ∠XYC is 73°. Find ∠YBA in Figure 2.
(a)
Area of Rectangle XZAC
= 22 x 12
= 264
Area of Triangle XYC
=
12 x 5 x 12
= 30 cm
2 Area of Triangle YCB
= (264 - 30 - 30) ÷ 2
= 204 ÷ 2
= 102 cm
2 Area of XYBAC
= 102 + 30 + 30
= 162 cm
2 (b)
∠CYB
= (180° - 73°) ÷ 2
= 107 ÷ 2
= 53.5° (Angles on a straight line)
∠YBA
= 360° - 90° - 90° - 53.5°
= 126.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 162 cm
2; (b) 126.5°