10.2.2 Perimeter and Area, PT3 Practice

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.

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, E and N are midpoints of AB, BC, CD and DA respectively.

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


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 6:
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.

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

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