Question

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

Answer 1

Answer:

Area of the frame = area of ( picture + frame) - area of picture

= ( 24 x 28 ) - (16 x 20)

= 672 - 320

= 342 sq. cm.

Answer 2

Given :-

Dimension of the outer frame = 24 cm × 28 cm

Dimension of the inner frame = 16 cm × 20 cm

To Find :-

The area of each section of the frame if the width of each section is same.

Solution :-

We know that,

• h = Height
• a = Area

(Refer to the attachment for your reference.)

I've divided the figure into 4 parts.

Now, here

Figures (I) and (II) are similar in dimensions. Even figures (III) and (IV) are similar in dimensions.

We know that,

Area of figure (I) = Area of trapezium

By the formula,

$\underline{\boxed{\sf Area \ of \ trapezium= \dfrac{1}{2} \times (a+b) \times h}}$

Substituting their values,

$\sf =\dfrac{1}{2} \times (28+20) \times 4$

$\sf =\dfrac{1}{2} \times 48 \times 4$

$\sf =96 \ cm^{2}$

Therefore,

Area of figure (I) = 96 cm²

Area of figure (II) = 96 cm²

We know that,

Area of figure (III) = Area of trapezium

By the formula,

$\sf Area \ of \ trapezium= \dfrac{1}{2} \times (a+b) \times h$

By substituting,

$\sf =\dfrac{1}{2} \times (24+16) \times 4$

$\sf =\dfrac{1}{2} \times 40 \times 4$

$\sf =80 \ cm^{2}$

Therefore,

Area of figure (III) = 80 cm²

Area of figure (IV) = 80 cm²