The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper JLMP that measures 21 cm by 16 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 78°. Find ∠KNM in Figure 2.
(a)
Area of Rectangle JLMP
= 21 x 16
= 336
Area of Triangle JKP
=
12 x 6 x 16
= 48 cm
2 Area of Triangle KPN
= (336 - 48 - 48) ÷ 2
= 240 ÷ 2
= 120 cm
2 Area of JKNMP
= 120 + 48 + 48
= 216 cm
2 (b)
∠PKN
= (180° - 78°) ÷ 2
= 102 ÷ 2
= 51° (Angles on a straight line)
∠KNM
= 360° - 90° - 90° - 51°
= 129° (Sum of angles in a quadrilateral)
Answer(s): (a) 216 cm
2; (b) 129°