11.2.2 Perimeter and Area, PT3 Practice


Question 5:
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 6:
In diagram below, ABCD and CGFE are rectangles. M, G, E and N are midpoints of AB, BC, CD and DA respectively.


Calculate the perimeter, in cm, of the coloured region.

Solution:


Using Pythagoras theorem M G 2 =M F 2 +F G 2         = 5 2 + 12 2         =25+144         =169 MG=13 cm Perimeter of the coloured region =13+13+5+12+5+12 =60 cm


Question 7:
Diagram below shows a trapezium BCDE and a parallelogram ABEF. ABC and FED are straight lines.

The area of ABEF is 72 cm2.
Calculate the area, in cm2, of trapezium BCDE.

Solution:
Base × Height =Area of ABFE 9 cm × Height=72  cm 2              Height= 72 9                         =8 cm CD=8 cm BC=239      =14 cm Area of trapezium BCDE = 1 2 ×( BC+ED )×CD = 1 2 ×( 14+9 )×8 =92  cm 2


Question 8:
In diagram below, ACEF is a trapezium and BCDG is a square.


Calculate the area, in cm2, of the coloured region.

Solution:
Area of trapezium ACEF = 1 2 ×( 8+15 )×10 =115  cm 2 Area of square BCDG =4×4 =16  cm 2 Area of trapezium GDEF = 1 2 ×( 4+15 )×6 =57  cm 2 Area of coloured region =1151657 =42  cm 2

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