The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper ACDF that measures 20 cm by 14 cm. AB = ED = 4 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 14
= 280
Area of Triangle ABF
=
12 x 4 x 14
= 28 cm
2 Area of Triangle BFE
= (280 - 28 - 28) ÷ 2
= 224 ÷ 2
= 112 cm
2 Area of ABEDF
= 112 + 28 + 28
= 168 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) 168 cm
2; (b) 129.5°