11. Split the following shapes into rectangles and find their areas. ( The measurement given in cm).
a.
in the above picture,
first let we name the corners as shown in the figure
here, we have to shapes into rectangle
so, to split the given shape into rectangles lets draw a line (in orange)
and name that as CX.
given, AB = 2cm
hence CX also 2cm
since ABCX forms rectangle (opposite sides are equal in length)
BC = 10cm which means AX = 10cm
1st rectangle ABXC
area of reactangle ABXC = 10 * 2
= 20 cm square
2nd rectangle XDFE
given, AD = 12, we knew AX = 10
so, XD = AD - AX = 12 - 10
XD = 2cm
XD = EF = 2cm
given, DF = 10cm
XE = XC + CE = 2 + 8 =10
so, XE = 10cm
now we know all the sides measurement
lets find its area now
Area of rectangle XDFE = 10 * 2
= 20 cm square
we have to find
Area of given shape = area of rectangle ABXC + area of rectangle XDFE
= 20 + 20
= 40 cm square.
b.
in the above figure
first let we name all the corners as ABCDEFGHIJKL
lets split the above shape into square ABLC, rectangle KDEJ and another square IFGH
Area of square ABLC = 7 * 7 = 49 cm square
Area of square IFGH = 7 * 7 = 49 cm square
Area of rectangle KDEJ
here, KD = KL + LC + CD = 7 + 7 + 7 = 21
Area of rectangle KDEJ = 21 * 7 = 147 cm square
Area of ABCDEFGHIJKL = Area of square ABLC + Area of square IFGH +
Area of rectangle KDEJ
= 49 + 49 + 147
= 245 cm square
c.
In the above figure,
lets first name the corners ABCDEFGH
we split the above given shape into two rectangles
ABCD and EFGH
Area of rectangle ABCD :
CD = CE + EF + FD = 2 + 1 + 2 = 5 ( GH = 1,so EF =1 )
AB = CD = 5 , AC = BD = 1
Area of rectangle ABCD = 5 * 1 = 5 cm square
Area of rectangle EFGH :
EF = GH = 1
EG = FG = 4
Area of rectangle EFGH = 1 * 4 = 4 cm square
Area of the given shape = Area of rectangle ABCD + Area of rectangle EFGH
= 5 + 4
= 9 cm square
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