Question

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

Answer 1

Area of trapezium $=\frac{1}{2}\times$(sum of parallel sides)$\times$ distance between the parallel sides

In figure,

Distance between the parallel sides of $I\&II=\frac{24cm-16cm}{2}=4cm$
Distance between the parallel sides of $III\&IV=\frac{28cm-20cm}{2}=4cm$

Area of section $I=$ Area of section $II$

$=\frac{1}{2}\times$(sum of parallel sides) $\times$ distance between the parallel sides

$=\frac{1}{2}\times 4cm(20cm+28cm)$

$=2cm\left(48cm\right)$

$=96c{m}^2$

Area of section $III=$ Area of section $IV$

$=\frac{1}{2}\times$ (sum of parallel sides) $\times$ distance between the parallel sides

$=\frac{1}{2}\times 4cm\times (16cm+24cm)$

$=2cm\times 40cm$

$=80c{m}^2$