Exercises: Area

For an Art project, Lucas needs a piece of card that measures exactly $2.400 \text{ cm}^2$. When he goes to the stationery store, the shop assistant tells him that the measurements are expressed in square decimeters. How many $\text{dm}^2$ should Lucas ask for for his project?

Calculate the area of the following shaded figure by counting the squares on the grid. Note that each small square represents an area of $1 \text{ m}^2$. Express the final result in square decameters ($\text{dam}^2$).

In the world of agriculture, special units are used. Match each International System measurement with its corresponding agricultural unit:

1. a) $1 \text{ hm}^2$
2. b) $1 \text{ dam}^2$
3. c) $1 \text{ m}^2$

I. Are ($a$)

II. Hectare ($ha$)

III. Centiare ($ca$)

A city council has decided to create a central park of $5 \text{ hectares}$. If they want to install a play area that occupies $1.500 \text{ m}^2$, how many square meters will be available for trees and paths in the rest of the park?

Select the most appropriate unit of measurement to express the area of the following objects:

1. a) The screen of a smartphone.
2. b) A professional soccer field.
3. c) The area of the United States.
4. d) The floor of your bedroom.

(Options: $km^2$, $hm^2$, $m^2$, $cm^2$)

A farmer has three plots with the following areas:

• Plot A: $0,45 \text{ hm}^2$

• Plot B: $5.200 \text{ m}^2$

• Plot C: $48 \text{ dam}^2$

Order the plots from smallest to largest area by comparing their measurements in $\text{m}^2$.

Express the following area measurement, given in mixed units, as a single unit in square meters:

$3 \text{ dam}^2$, $25 \text{ m}^2$ and $75 \text{ dm}^2$

In a residential development, a square communal area measuring $10 \text{ meters}$ per side is going to be paved. Square tiles with an area of $1 \text{ dm}^2$ each will be used. How many tiles will be needed to cover the whole area?

A city council is planning the creation of a new suburban park. They have bought three adjacent plots whose areas are expressed in different units:

• Plot A: $0,052\text{ km}^2$

• Plot B: $140\text{ dam}^2$

• Plot C: $8.500\text{ m}^2$

Express the total area of the future park in hectares ($ha$).

The screen of a new tablet model has dimensions of $250\text{ mm}$ high by $160\text{ mm}$ wide. The manufacturer claims that the usable area of the screen is exactly $4\text{ dm}^2$. Is the manufacturer's claim true? Justify your answer by carrying out the necessary calculations in $\text{cm}^2$.

A forest fire has affected an area of the mountain range. The news indicates that $12\text{ km}^2$ and $45\text{ hm}^2$ of forest have been burnt. To organize the reforestation, the forestry technicians need to know the affected area in ares ($a$) and centiares ($ca$). Carry out the conversion to both units.

We want to change the floor of a kitchen that has a rectangular shape and measures $420\text{ cm}$ long by $3\text{ m}$ wide. If we are going to use square tiles with an area of $20\text{ dm}^2$ each:

1. a) Calculate the total area of the kitchen in $\text{m}^2$.
2. b) How many tiles will we need to cover the whole floor?

Order the following areas of nature reserves from largest to smallest, first converting them all to the same unit (whichever you prefer):

• Reserve A: $12.400.000\text{ m}^2$

• Reserve B: $1.350\text{ ha}$

• Reserve C: $128\text{ km}^2$

• Reserve D: $1.250.000\text{ dam}^2$

A farmer has a farm of $3\text{ ha}$, $5\text{ a}$ and $25\text{ ca}$. They decide to sell a part of their land for the construction of a road. The sold part measures exactly $4.200\text{ m}^2$. What area of the farm, expressed in mixed units (hectares, ares and centiares), does the farmer have left?

On a scale plan of a shopping center, the central aisle is represented by a rectangle with an area of $450\text{ cm}^2$. If we know that in reality this aisle occupies $0,18\text{ dam}^2$:

1. a) Express both quantities in $\text{dm}^2$.
2. b) How many times larger is the real area than the area on the plan?

Calculate the area of the following irregular figure by breaking it down into squares and rectangles. Each square on the background grid represents an area of $100\text{ cm}^2$. Express the final result in square decimeters ($\text{dm}^2$).

A wine company has bought a plot of land to plant vineyards that has an area of $0,12 \text{ km}^2$ and $5,4 \text{ hm}^2$. To make better use of the land, they divide it into plots of $60 \text{ áreas}$ each. If each of these plots produces an average of $850 \text{ kg}$ of grapes and the market price of grapes is $\$0,75 \text{ \$/kg}$, calculate the total value of the production of the entire land in one harvest.

For the construction of a new shopping center, a rectangular plot measuring $2,4 \text{ hm}$ long and $150 \text{ m}$ wide has been fenced off. The local council requires $25 \%$ of the total area to be dedicated to green areas and another $15 \%$ to parking lots. If the rest is divided into commercial units with an average area of $120 \text{ m}^2$, how many units can be built in total?

An artist wants to cover the side facade of a building with square solar panels of side $50 \text{ cm}$. The facade is a rectangle $12 \text{ m}$ high and $3,5 \text{ dam}$ long, but 8 symmetrical windows measuring $150 \text{ dm}^2$ each must be subtracted. Calculate the total number of solar panels they need to buy to cover the entire available surface of the facade.

In a reforestation plan after a fire, work will be carried out on an area of $14 \text{ ha}, 5 \text{ a}$ and $20 \text{ ca}$. Forestry engineers have decided that one tree must be planted for every $12 \text{ m}^2$ of land. If the cost of each sapling is $\$4,80 \text{ \$}$ and labor costs $\$250 \text{ \$}$ for each square decameter worked, what will be the total budget needed for the reforestation?

A graphic designer is creating a logo on a metal sheet. The logo consists of a central square with an area of $4 \text{ dm}^2$. Around this square, they add four smaller squares whose sides are half the length of the side of the central square. Express the total area of the logo in square millimeters and in square decimeters using only a single unit.

A map of a nature reserve has a scale such that $1 \text{ cm}^2$ on paper represents $2.500 \text{ m}^2$ in reality. If the reserve has an irregular shape that occupies $480 \text{ cm}^2$ on the map, calculate its real area in hectares, ares and centiares (mixed units). If a fire destroys $0,4 \text{ km}^2$ of the reserve, what percentage of the total area has been saved?

The floor of a sports center with an area of $12,5 \text{ dam}^2$ is going to be renovated. Boxes of heavy-duty tiles have been bought, where each box contains enough material to cover $2,5 \text{ m}^2$ and costs $\$45 \text{ \$}$. In addition to the cost of the material, the installation company charges $\$18 \text{ \$}$ for each square meter laid. What is the total bill if $5 \%$ more material than needed is bought to make up for what is wasted in cuts and breakages?

Calculate the total area of the following figure made of metal parts. The main part is a rectangle of $0,8 \text{ m}$ by $15 \text{ cm}$, to which square tabs of side $25 \text{ mm}$ have been welded at each of its four vertices. In addition, a circular hole with an area of $450 \text{ mm}^2$ has been made in the center. Express the final result in square centimeters, rounding to the nearest whole number.