Question

find the measures of given plots. (All measures in metres)

Answer 1

Answer:

Here, ∆QAP, ∆RCS are right angled triangles and QACR is a trapezium.  

In ∆QAP,

l(AP) = 30 m, l(QA) = 50 m  

A(∆QAP) = (1/2) x product of sides forming the right angle  

= (1/2) x l(AP) x l(QA)  

= (1/2) x 30 x 50 = 750 sq. m  

In QACR,

l(QA) = 50 m, l(RC) = 25 m,  

l(AC) = l(AB) + l(BC) = 30 + 30 = 60 m  

A(QACR) = (1/2) x sum of lengths of parallel sides x height  

= (1/2) x [l(QA) + l(RC)] x l(AC)  

= (1/2) x (50 + 25) x 60  

= (1/2) x 75 x 60 = 2250 sq.m  

In ∆RCS,

l(CS) = 60 m, l(RC) = 25 m

A(∆RCS) = (1/2) x product of sides forming the right angle  

= (1/2) x l(CS) x l(RC)  

= (1/2) x 60 x 25 = 750 sq. m  

In ∆PTS,

l(TB) = 30 m,  l(PS) = l(PA) + l(AB) + l(BC) + l(CS) = 30 + 30 + 30 + 60  

= 150m  

A(∆PTS) = (1/2) x base x height

= (1/2) x l(PS) x l(TB)  

= (1/2) x 150 x 30

= 2250 sq. m  

∴ Area of plot QPTSR = A(∆QAP) + A(QACR) + A(∆RCS) + A(∆PTS)  

= 750 + 2250 + 750 + 2250

= 6000 sq. m  

∴ The area of the given plot is 6000 sq.m

Step-by-step explanation:

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