Ncert solutions

# Question 11

Q11.Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.

Solution 11:

Let the outer quadrilateral in the frame be ABCD

Let the inner quadrilateral be PQRS

Let the width marked be as in the figure,equal

PL=PK=QM=QN=RG=RH=SI=JS

BC=28cm, QM=RH (equal width)

QR=20cm

QM+QR+RH=BC

QM+20+QM=28

2 QM=28-20

QM=4 CM

In the figure,

1. Area of trapezium QBCR=Area of trapezium APSD

=48\times2

=96\ cm^2

1. Area of trapezium SRCD =Area of trapezium ABQP

\frac{1}{2}\times\left(CD+RS\right)\times RH=\frac{1}{2}\left(24+16\right)\times4

=\frac{1}{2}\times32\times4

=64\ cm^2

Area of frame=2{(area of trapezium QBCR)+(area of trapezium SRCD)}

=2(96+64)

=2(160)

=320\ cm^2

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