Question

Diagram of the adjacent picture frame has outer dimension = 24 cm x 28 cm and inner dimension 16cm x 20cm .find the area of each sections of the frame , if the width of each sections is same

Answer 1

$16 + 2x = 24 \\ 2x = 8 \\ x = 4 \\ area \: of \: first \: frem = \frac{1}{2} \times (20 + 28) \times 4 = 48 \times 2 = 96 {cm}^{2} \\ area \: of \: second \: frem = \frac{1}{2} \times (16 + 24) \times 4 = 40 \times 2 = 80 {cm}^{2}$

Answer 2

Answer:

Area of trapezoid 1=80 cm²

Area of trapezoid 2=96 cm²

Area of trapezoid 3=80 cm²

Area of trapezoid 4=96 cm²

Step-by-step explanation:

We are given two rectangles. One inside the another.

Length of outer rectangle is 24 cm

Length of inner rectangle is 16 cm

Let one side width be x

2x=24-16

x=4 cm

In diagram, we can see 4 trapezium form whose height is 4 cm

Area of trapezium = $\frac{1}{2}\times$sum of parallel sides x height

Trapezium 1, Length of parallel sides are 24 cm and 16 cm, Height is 4 cm.  

$\text{Area of trapezoid 1}=\frac{1}{2}\times (24+16)\times 4 = 80\text{ cm}^2$

Trapezium 2, Length of parallel sides are 28 cm and 20 cm, Height is 4 cm.  

$\text{Area of trapezoid 2}=\frac{1}{2}\times (28+20)\times 4 = 96\text{ cm}^2$

Trapezium 3, Length of parallel sides are 24 cm and 16 cm, Height is 4 cm.  

$\text{Area of trapezoid 3}=\frac{1}{2}\times (24+16)\times 4 = 80\text{ cm}^2$

Trapezium 4, Length of parallel sides are 28 cm and 20 cm, Height is 4 cm.  

$\text{Area of trapezoid 4}=\frac{1}{2}\times (28+20)\times 4 = 96\text{ cm}^2$