The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper QSTV that measures 18 cm by 16 cm. QR = UT = 5 cm. The paper is folded along the dotted line RU such that point S touches point V, as shown in Figure 2.
- Find the area of Figure 2. QRUTV, after the folding.
- In Figure 2, ∠QRV is 77°. Find ∠RUT in Figure 2.
(a)
Area of Rectangle QSTV
= 18 x 16
= 288
Area of Triangle QRV
=
12 x 5 x 16
= 40 cm
2 Area of Triangle RVU
= (288 - 40 - 40) ÷ 2
= 208 ÷ 2
= 104 cm
2 Area of QRUTV
= 104 + 40 + 40
= 184 cm
2 (b)
∠VRU
= (180° - 77°) ÷ 2
= 103 ÷ 2
= 51.5° (Angles on a straight line)
∠RUT
= 360° - 90° - 90° - 51.5°
= 128.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 184 cm
2; (b) 128.5°