Question

a picture of dimension 30 cm by 18 cm has a wooden frame of width 1.5 around it . find the area of the frame by dividing it into four trapezium . verify your answer by finding the difference of the rectangular areas of the picture with and without the frame​

Answer 1

Answer:

Area = 153 cm square

Step-by-step explanation:

Formula for area of trapezium;

A = ( length of one side + length of opposite side) / 2 x height

IN our case;

A = ( 30 + 33) / 2 x 1.5

A = 47.25 this is for side with length 30 cm

Now for side with length 18

A = ( 18 + 21) / 2 x 1.5

A = 29.25

Total area of frame;

Area = 47.25 + 47.25 + 29.25 + 29.25 = 153

Now using the second method;

Area of picture = length x height

Area of picture = 30 x 18 = 540

Area of frame and picture = 33 x 21 = 693

Area of frame only = 693 – 540 = 153

Answer 2

AB = (18+1.5×2) =21cm

Area of trapezium AHCB = Area of BCFE = ½{ (18+21)×1.5 } cm² = 29.25cm²

BC = (30+1.5×2) cm = 33cm

Area of trapezium AHED = Area of BCFG = ½ {(33+30)×1.5} = 47.25 cm²

Area of frame = (29.25+29.25+47.25+47.25) = 153cm²

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