The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper FHJL that measures 18 cm by 15 cm. FG = KJ = 4 cm. The paper is folded along the dotted line GK such that point H touches point L, as shown in Figure 2.
- Find the area of Figure 2. FGKJL, after the folding.
- In Figure 2, ∠FGL is 72°. Find ∠GKJ in Figure 2.
(a)
Area of Rectangle FHJL
= 18 x 15
= 270
Area of Triangle FGL
=
12 x 4 x 15
= 30 cm
2 Area of Triangle GLK
= (270 - 30 - 30) ÷ 2
= 210 ÷ 2
= 105 cm
2 Area of FGKJL
= 105 + 30 + 30
= 165 cm
2 (b)
∠LGK
= (180° - 72°) ÷ 2
= 108 ÷ 2
= 54° (Angles on a straight line)
∠GKJ
= 360° - 90° - 90° - 54°
= 126° (Sum of angles in a quadrilateral)
Answer(s): (a) 165 cm
2; (b) 126°