Question

A, B, C and D are the mid-points of sides of parallelogram PQRS. If ar(PQRS) = 45 cm², then find ar(ABCD)

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Answer 1

Answer:

A,B,C,D are point of sides of parallelogram PQRS area (PQRS)=36 cm

2

ar(ABCD)=?

AP=

2

1

SP, BP=

1

QR

PS=QR,

2

1

PS=

2

1

QR

area (△ABC)=

2

1

(△PQCQ)

area (△ADC)=

2

1

ar(ACRS)

area △ABC+area(△ADC)=

2

1

area(APCQ)=

2

1

area(ACRS)

area(ADCD)=

2

1

area(APCQ)+(ACRS)area

area(ABCD)=

2

1

area(PQRS)

area(ABCD)=

2

1

(36)

=18 cm

2

Answer 2

Answer:

A,B,C,D are point of sides of parallelogram PQRS area (PQRS)=36 cm

2ar(ABCD)=?

AP=1/2SP,BP= 1QR

PS=QR, 1/2, PS=1/2QR

area (△ABC)=1/2(△PQCQ)

area (△ADC)=1/2ar(ACRS)

area △ABC+area(△ADC)=1/2 area(APCQ)=1/2 area(ACRS)

area(ADCD)= 1/2area(APCQ)+(ACRS)area

area(ABCD)= 1/2 area(PQRS)

area(ABCD)=1/2 45

area(ABCD)=22.5

​Step-by-step explanation:

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