Perimeter and areaIB MYP Maths Standard: Subtopic test

1. 1
   A sector $OAB$ of a circle has centre $O$, radius $12$ cm and angle $AOB=75^\circ$. Use the $\pi$ button on your calculator.

   (a)

   Find the length of arc $AB$.

   [1 mark]

   • A$75.4$ cm
   • B$94.2$ cm
   • C$7.85$ cm
   • D$15.7$ cm

   (b)

   Find the area of the sector.

   [1 mark]

   • A$15.7$ cm$^2$
   • B$452.4$ cm$^2$
   • C$94.2$ cm$^2$
   • D$188.5$ cm$^2$

   (c)

   Find the perimeter of the sector.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A trapezium has parallel sides of length $9$ cm and $15$ cm. The perpendicular distance between the parallel sides is $6$ cm.

   (a)

   Find the area of the trapezium.

   [1 mark]

   • A$72$ cm$^2$
   • B$144$ cm$^2$
   • C$90$ cm$^2$
   • D$54$ cm$^2$

   (b)

   A parallelogram has the same area as the trapezium and a base of $12$ cm. Find its perpendicular height.

   [1 mark]

   • A$864$ cm
   • B$6$ cm
   • C$3$ cm
   • D$60$ cm

   (c)

   A triangle has a base of $15$ cm and the same area as the trapezium. Find its perpendicular height.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A window is made from a rectangle $1.2$ m wide and $1.5$ m high, with an isosceles triangle on top. The triangle has a base of $1.2$ m, a perpendicular height of $0.5$ m, and each of its sloping sides is $0.78$ m long.

   (a)

   Find the total area of the window.

   [3 marks]

   (b)

   A decorative trim is fitted around the whole outside edge of the window. It costs AED $24$ per metre. Find the perimeter of the window and the cost of the trim.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A school running track has two straight sections, each $80$ m long, joined by two semicircular ends. The straight sections are $40$ m apart, so each semicircle has a diameter of $40$ m.

   (a)

   (i) Find the distance once around the track.
   (ii) A runner must run at least $1500$ m. Find the number of complete laps needed.
   (iii) Find the area enclosed by the track.

   [6 marks]

   (b)

   The school considers lengthening each straight section from $80$ m to $100$ m, keeping the same semicircular ends. A pupil says: 'The straights are $25\%$ longer, so both the distance around the track and the area enclosed will increase by $25\%$.'
   (i) Find the new distance around the track.
   (ii) Find the new area enclosed.
   (iii) Show that the pupil is wrong.

   [6 marks]

   Total for question 4: 12 marks

End of questions