The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper JLMP that measures 22 cm by 14 cm. JK = NM = 5 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 72°. Find ∠KNM in Figure 2.
(a)
Area of Rectangle JLMP
= 22 x 14
= 308
Area of Triangle JKP
=
12 x 5 x 14
= 35 cm
2 Area of Triangle KPN
= (308 - 35 - 35) ÷ 2
= 238 ÷ 2
= 119 cm
2 Area of JKNMP
= 119 + 35 + 35
= 189 cm
2 (b)
∠PKN
= (180° - 72°) ÷ 2
= 108 ÷ 2
= 54° (Angles on a straight line)
∠KNM
= 360° - 90° - 90° - 54°
= 126° (Sum of angles in a quadrilateral)
Answer(s): (a) 189 cm
2; (b) 126°