Here is a shape ABCD. Calculate the perimeter of the shape.
Give your answer correct to 3
significant figures.
B
С
D
9 cm
O
9 cm
140°
21 cm
24°
А
The shape is made from a triangle and a
sector of a circle, centre O and radius 9 cm.
AD = 21 cm
Angle AOD = 140°
Angle OAD = 24°
Total marks: 5

9514 1404 393

  59.8 cm

Step-by-step explanation:

The length of arc ABC is ...

  s = rθ

  s = (9 cm)(220/180π) = 11π cm ≈ 34.558 cm

The length of segment CD is 9 cm less than the length of segment OD. OD can be found using the law of sines.

  OD/sin(A) = AD/sin(O)

  OD = AD·sin(A)/sin(O) = (21 cm)sin(24°)/sin(140°) ≈ 13.288 cm

Then the length of CD is ...

  CD = OD -9 cm = (13.288 cm) -(9 cm) = 4.288 cm

The perimeter is the sum of the segment and arc lengths:

  P = ABC + CD +AD

  P = 34.558 cm + 4.288 cm + 21 cm = 59.846 cm

The perimeter of the shape is about 59.8 cm.