The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper KMNQ that measures 22 cm by 15 cm. KL = PN = 6 cm. The paper is folded along the dotted line LP such that point M touches point Q, as shown in Figure 2.
- Find the area of Figure 2. KLPNQ, after the folding.
- In Figure 2, ∠KLQ is 78°. Find ∠LPN in Figure 2.
(a)
Area of Rectangle KMNQ
= 22 x 15
= 330
Area of Triangle KLQ
=
12 x 6 x 15
= 45 cm
2 Area of Triangle LQP
= (330 - 45 - 45) ÷ 2
= 240 ÷ 2
= 120 cm
2 Area of KLPNQ
= 120 + 45 + 45
= 210 cm
2 (b)
∠QLP
= (180° - 78°) ÷ 2
= 102 ÷ 2
= 51° (Angles on a straight line)
∠LPN
= 360° - 90° - 90° - 51°
= 129° (Sum of angles in a quadrilateral)
Answer(s): (a) 210 cm
2; (b) 129°