The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper JLMP that measures 19 cm by 14 cm. JK = NM = 6 cm. The paper is folded along the dotted line KN such that point L touches point P, as shown in Figure 2.
- Find the area of Figure 2. JKNMP, after the folding.
- In Figure 2, ∠JKP is 79°. Find ∠KNM in Figure 2.
(a)
Area of Rectangle JLMP
= 19 x 14
= 266
Area of Triangle JKP
=
12 x 6 x 14
= 42 cm
2 Area of Triangle KPN
= (266 - 42 - 42) ÷ 2
= 182 ÷ 2
= 91 cm
2 Area of JKNMP
= 91 + 42 + 42
= 175 cm
2 (b)
∠PKN
= (180° - 79°) ÷ 2
= 101 ÷ 2
= 50.5° (Angles on a straight line)
∠KNM
= 360° - 90° - 90° - 50.5°
= 129.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 175 cm
2; (b) 129.5°