Question

A square vegetable garden has side lengths of 12 feet. You plant flowers in the center portion as shown. You divide the remaining space into 4 equal sections and plant tomatoes, onions, zucchini, and peppers. What is the area of the onion section???

Answer 1

Given :-

• A square vegetable garden has side lengths of 12 feet.
• You plant flowers in the center portion of the garden,a square that has side lengths of 4 feet.
• You divide the remaining space into 4 equal sections and plant tomatoes, onions, zucchini, and peppers.

To Find :-

• What is the area of the onion section ?

Solution :-

Given that,

→ side of square vegetable garden is = 12 feet .

So ,

→ Area of square vegetable garden = (side)² = (12)² = 144 feet².

Now, given that, inside this area, there is a square of side 4 feet reserved for flowers .

So,

→ The area of the flower section = (side)² = (4)² = 16 feet².

Therefore,

→ The rest of the garden that is intended for vegetables is = The total garden area - The flower section area = 144 - 16 = 128 feet².

Now, this remaining area is to be divided in four equal sections .

So,

→ The area of the onion section = (1/4) of remaining area = (1/4) * 128 = 32 feet². (Ans.)

Hence, The area of the onion section is 32 feet².

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Answer 2

✴ Given :

A square vegetable garden has side lengths of 14 feet. You plant flowers in the center portion of the garden, a square that has side lengths of 4 feet. You divide the remaining space into 4 equal sections and plant tomatoes, onions, zucchini, and peppers.

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✴ To Find :

What is the area of the onion section?

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✴ Solution :

✏ Concept :

We will use the concept of Area here .By using the formula Area of square we will wind the area of whole garden. After that we will find the area of middle portion planted flowers. When we will subtract total area - planted flowers we will get the remaining area .By dividing the remaining area into 4 parts we can get the area of onion section. Let's Solve :

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

✏ Formula Used :

$\large{\orange{\bigstar}} \: \: \: {\underline{\boxed{\red{\sf{ Area{\small_{(Square) }} = Side \times Side}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

✏ Area of whole field :

$\twoheadrightarrow{\qquad{\sf{ Area{\small_{(Whole \: field) }} = Side \times Side}}}$

$\twoheadrightarrow{\qquad{\sf{ Area{\small_{(Whole \: field) }} = 14 \times 14}}}$

${:\longmapsto{\sf{ Area \: of \: Whole \: field = {\green{\sf{ 196 \: feet}}}}}}$

✏ Area of planted flowers :

$\twoheadrightarrow{\qquad{\sf{ Area{\small_{(Planted \: flowers) }} = Side \times Side}}}$

$\twoheadrightarrow{\qquad{\sf{ Area{\small_{(Planted \: flowers) }} = 4 \times 4}}}$

${:\longmapsto{\sf{ Area \: of \: Planted \: flowers = {\color{orange}{\sf{ 16 \: feet}}}}}}$

✏ Area Left :

$\twoheadrightarrow{\qquad{\sf{ Area{\small_{(Left) }} = Total \: Area - Planted \: flowers}}}$

$\twoheadrightarrow{\qquad{\sf{ Area{\small_{(Left) }} = 196 - 16}}}$

${:\longmapsto{\sf{ Area \: left = {\color{red}{\sf{ 180 \: feet }}}}}}$

✏ Area of onion section :

$\twoheadrightarrow{\qquad{\sf{ Area{\small_{(Onion \: Section) }} = \dfrac{Area \: left}{4}}}}$

$\twoheadrightarrow{\qquad{\sf{ Area{\small_{(Onion \: Section) }} = \dfrac{180}{4}}}}$

$\twoheadrightarrow{\qquad{\sf{ Area{\small_{(Onion \: Section) }} = \cancel\dfrac{180}{4}}}}$

${:\longmapsto{\sf{ Area \: left = {\color{red}{\sf{ 45 \: feet²}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

Therefore :

$❝{\sf{ Area \: of \: onion \: section \: is }}{\pink{\underline{\orange{\sf{ \: 45 feet²}}}}}. ❞$

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✬ Note :

Refer to attachment for better explanation.