Question

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. What is the area of the onion section?

Answer 1

✴ 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 :

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

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

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

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

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

Therefore :

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

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✬ Note :

Refer to attachment for better explanation.

Answer 2

Step-by-step explanation:

The total area for garden is the area of a square with side 14 ft.

That means the garden's total area is the square of its side:

Area of a square of side "

$\tt\large\underline\purple{x" = x*x=x^2x∗x=x2 ,}$

then for our case where the square's side is 14 ft, the square's area becomes: 

$Area=(14\,ft)^2 = 196\, ft^2Area=(14ft)2=196ft2$

Inside this area, there is a square of side 4 ft reserved for flowers (and what is left -the rest- for veggies). The area of the flower section is then: 

$(4\,ft)^2=16\,ft^2(4ft)2=16ft2 .$

Therefore the rest of the garden that is intended for veggies is (the total garden area minus the flower section area)

$= 196\,ft^2-16\,ft^2=180\,ft^2196ft2−16ft2=180ft2$

This remaining veggie are is to be divided in four (4) equal parts, and one of them destined for tomato plants. The area of each of the veggie sections is one fourth of the remaining area: \

$\frac{180\,ft^2}{4} =45\, ft^24180ft2=45ft2$

• $\:$
• So in particular the tomato plant area is 45 ft^2ft2

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