The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper DFGJ that measures 21 cm by 12 cm. DE = HG = 4 cm. The paper is folded along the dotted line EH such that point F touches point J, as shown in Figure 2.
- Find the area of Figure 2. DEHGJ, after the folding.
- In Figure 2, ∠DEJ is 75°. Find ∠EHG in Figure 2.
(a)
Area of Rectangle DFGJ
= 21 x 12
= 252
Area of Triangle DEJ
=
12 x 4 x 12
= 24 cm
2 Area of Triangle EJH
= (252 - 24 - 24) ÷ 2
= 204 ÷ 2
= 102 cm
2 Area of DEHGJ
= 102 + 24 + 24
= 150 cm
2 (b)
∠JEH
= (180° - 75°) ÷ 2
= 105 ÷ 2
= 52.5° (Angles on a straight line)
∠EHG
= 360° - 90° - 90° - 52.5°
= 127.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 150 cm
2; (b) 127.5°