The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper JLMP that measures 22 cm by 12 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 80°. Find ∠KNM in Figure 2.
(a)
Area of Rectangle JLMP
= 22 x 12
= 264
Area of Triangle JKP
=
12 x 6 x 12
= 36 cm
2 Area of Triangle KPN
= (264 - 36 - 36) ÷ 2
= 192 ÷ 2
= 96 cm
2 Area of JKNMP
= 96 + 36 + 36
= 168 cm
2 (b)
∠PKN
= (180° - 80°) ÷ 2
= 100 ÷ 2
= 50° (Angles on a straight line)
∠KNM
= 360° - 90° - 90° - 50°
= 130° (Sum of angles in a quadrilateral)
Answer(s): (a) 168 cm
2; (b) 130°