Perimeter and Area

Question 7: In diagram below, AEC is a right-angled triangle with an area of 54 cm2 and BCDF is a rectangle. Calculate (a) the perimeter, in cm, of the coloured region. (b) the area, in cm2, of the coloured region. Solution: (a) Given area of △ ACE 1 2 ×AC×9=54    AC=54× 2 9    AC=12 cm Using Pythagoras’ theorem: AE= 9 2 + … Read more

Question 4: In diagram below, PQUV is a square, QRTU is a rectangle and RST is an equilateral triangle. The perimeter of the whole diagram is 310 cm. Calculate the length, in cm, of PV. Solution: PV=VU=TS=SR=QP Given perimeter of the whole diagram=310 cm PV+VU+UT+TS+SR+RQ+QP=310 PV+PV+50+PV+PV+50+PV=310 5PV+100=310  5PV=210    PV=42 cm Question 5: In diagram below, ABCD and CGFE are rectangles. M, G, … Read more

Question 1: In the diagram, ABCD is a trapezium and ABEF is a parallelogram. Calculate the area, in cm2, of the coloured region. Solution: Area of trapezium ABCD = 1 2 ×( 8+14 )×10 =110  cm 2 Area of parallelogram ABEF =8×6 =48  cm 2 Area of the shaded region =110−48 =62  cm 2 Question 2: Diagram below shows a rectangle ABCD. Calculate the area, … Read more

Question 12: Diagram shows a quadrant KLM with centre  M and sector JMN with centre J. Using π = 22 7 , calculate (a) the perimeter, in cm, of the whole diagram, (b) the area, in cm2, of the shaded region.  [6 marks] Solution: (a) KM2 = JK2 + JM2 KM2 = 32+ 42 KM2 = … Read more

Question 9: In diagram below, ADB is a right-angled triangle and DBFE is a square. C is the midpoint of DB and CH = CD. Calculate the area, in cm2, of the coloured region. Solution: Area of △ ABC = 1 2 ×6×8 =24  cm 2 Area of trapezium BCHF = 1 2 ×( 12+6 )×6 =54  cm 2 Area of CDEFH =( … Read more