The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper ACDF that measures 20 cm by 12 cm. AB = ED = 6 cm. The paper is folded along the dotted line BE such that point C touches point F, as shown in Figure 2.
- Find the area of Figure 2. ABEDF, after the folding.
- In Figure 2, ∠ABF is 79°. Find ∠BED in Figure 2.
(a)
Area of Rectangle ACDF
= 20 x 12
= 240
Area of Triangle ABF
=
12 x 6 x 12
= 36 cm
2 Area of Triangle BFE
= (240 - 36 - 36) ÷ 2
= 168 ÷ 2
= 84 cm
2 Area of ABEDF
= 84 + 36 + 36
= 156 cm
2 (b)
∠FBE
= (180° - 79°) ÷ 2
= 101 ÷ 2
= 50.5° (Angles on a straight line)
∠BED
= 360° - 90° - 90° - 50.5°
= 129.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 156 cm
2; (b) 129.5°