Question

Martha bought a photo frame with a perimeter of 36 cm. if the frame is 10 cm wide find the area of frame
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Answer 1

Given :

• Martha bought a photo frame with a perimeter of 36 cm. The frame is 10 cm wide.

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To Find :

• Find the area of the frame.

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Solution :

~ Formula Used :

$\large{\red{\bigstar}} \: \: {\underline{\boxed{\purple{\sf{ Perimeter{\small_{(Rectangle) }} = 2(Length + Breath) }}}}}$

$\large{\red{\bigstar}} \: \: {\underline{\boxed{\purple{\sf{ Area{\small_{(Rectangle) }} = Length \times Breath }}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

~ Calculating the Length of Frame :

Here we have :

• ➵ Perimeter = 36 cm
• ➵ Breadth = 10 cm
• ➵ Length = ?

Let's Calculate :

${\longmapsto{\qquad{\sf{ Perimeter = 2(Length + Breadth) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 36 = 2(Length + 10)}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 36 = 2Length + 20 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 36 - 20 = 2Length }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 16 = 2Length }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{16}{2} = Length }}}} \\ \\ \ {\qquad{\textsf{ Length of the Frame = {\pink{\sf{ 8 \: cm}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

~ Calculating the Area of Frame :

Here we have :

• ➵ Area = ?
• ➵ Length = 8 cm
• ➵ Breadth = 10 cm

Let's Calculate :

${\longmapsto{\qquad{\sf{ Area = Length \times Breadth }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area = 10 \times 8 }}}} \\ \\ \ {\qquad{\textsf{ Area of the Frame = {\blue{\sf{ 80 \: cm²}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

~ Therefore :

❝ Area of the frame is 80 cm² .❞

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Answer 2

Answer:

80cm².

Step-by-step explanation:

First we will calculate length using perimeter and width and after that we will calculate area using length and width. So, let's start :-

Calculating Length

It is given that,

Perimeter = 36cm.

Width = 10cm

Length = ?

Perimeter = 2(l + w)

Put known values in the above formula.

⟹ 36 = 2(l + 10)

⟹ 36 = 2l + 20

⟹ 2l + 20 = 36

⟹ 2l = 36 - 20

⟹ 2l = 16

⟹ l = $\rm\dfrac{16}{2}$

∴ Length = 8cm.

Now, we will calculate area of frame

Length = 8cm

Width = 10cm

Area = Length × Width

⟹ Area = 8 × 10

⟹ Area = 80cm².

Hence, area of the frame is 80cm².