The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper DFGJ that measures 19 cm by 15 cm. DE = HG = 5 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 80°. Find ∠EHG in Figure 2.
(a)
Area of Rectangle DFGJ
= 19 x 15
= 285
Area of Triangle DEJ
=
12 x 5 x 15
= 37.5 cm
2 Area of Triangle EJH
= (285 - 37.5 - 37.5) ÷ 2
= 210 ÷ 2
= 105 cm
2 Area of DEHGJ
= 105 + 37.5 + 37.5
= 180 cm
2 (b)
∠JEH
= (180° - 80°) ÷ 2
= 100 ÷ 2
= 50° (Angles on a straight line)
∠EHG
= 360° - 90° - 90° - 50°
= 130° (Sum of angles in a quadrilateral)
Answer(s): (a) 180 cm
2; (b) 130°