The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper XZAC that measures 21 cm by 14 cm. XY = BA = 6 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 76°. Find ∠YBA in Figure 2.
(a)
Area of Rectangle XZAC
= 21 x 14
= 294
Area of Triangle XYC
=
12 x 6 x 14
= 42 cm
2 Area of Triangle YCB
= (294 - 42 - 42) ÷ 2
= 210 ÷ 2
= 105 cm
2 Area of XYBAC
= 105 + 42 + 42
= 189 cm
2 (b)
∠CYB
= (180° - 76°) ÷ 2
= 104 ÷ 2
= 52° (Angles on a straight line)
∠YBA
= 360° - 90° - 90° - 52°
= 128° (Sum of angles in a quadrilateral)
Answer(s): (a) 189 cm
2; (b) 128°