The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper ZBCE that measures 18 cm by 12 cm. ZA = DC = 6 cm. The paper is folded along the dotted line AD such that point B touches point E, as shown in Figure 2.
- Find the area of Figure 2. ZADCE, after the folding.
- In Figure 2, ∠ZAE is 72°. Find ∠ADC in Figure 2.
(a)
Area of Rectangle ZBCE
= 18 x 12
= 216
Area of Triangle ZAE
=
12 x 6 x 12
= 36 cm
2 Area of Triangle AED
= (216 - 36 - 36) ÷ 2
= 144 ÷ 2
= 72 cm
2 Area of ZADCE
= 72 + 36 + 36
= 144 cm
2 (b)
∠EAD
= (180° - 72°) ÷ 2
= 108 ÷ 2
= 54° (Angles on a straight line)
∠ADC
= 360° - 90° - 90° - 54°
= 126° (Sum of angles in a quadrilateral)
Answer(s): (a) 144 cm
2; (b) 126°