11.2.1 Perimeter and Area, PT3 Practice


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 =11048 =62  cm 2


Question 2:
Diagram below shows a rectangle ABCD.


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

Solution:

The area of the coloured region =Area of rectangleArea of trapezium =( 12×8 ) 1 2 ×( 4+6 )×4 =9620 =76  cm 2


Question 3:
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 + 12 2   =15 cm Perimeter of coloured region =6+4.5+6+4.5+15 =36 cm

(b) Area of the coloured region =Area of  ACEArea of rectangle BCDF =54( 6×4.5 ) =5427 =27  cm 2


Question 4:
Diagram below shows a trapezium ABCDE. ABGF is a square with an area of 36 cm2.


Calculate
(a) the perimeter, in cm, of the coloured region.
(b) the area, in cm2, of the coloured region.

Solution:

(a) Using Pythagoras’ theorem: In  CDH, CD= 8 2 + 6 2  =10 cm AB=BG=GF=FA= 36 =6 cm Perimeter of coloured region =6+10+18+2+6+6 =48 cm

(b) Area of the coloured region =Area of trapezium ABCDEArea of square ABGF =[ 1 2 ( 12+18 )×8 ]36 =[ 1 2 ×30×8 ]36 =12036 =84  cm 2

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