Surface Measurements

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 top-division soccer field.
3. c) The surface area of the Dominican Republic.
4. d) The floor of your bedroom.

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

For an art project, Lucas needs a piece of card that measures exactly $2,400 \text{ cm}^2$. When he goes to the stationer's, the shop assistant tells him that measurements are given in square decimeters. How many $\text{dm}^2$ should Lucas ask for for his project?

Express in simple form (using a single unit) in square meters the following area measurement given in compound form:

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

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 $\text{m}^2$.

A local municipality 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 ($ha$).

Order the following areas of natural parks in the Dominican Republic from largest to smallest, first converting them all to the same unit of your choice:

• Park A: $12,400,000\text{ m}^2$

• Park B: $1,350\text{ ha}$

• Park C: $128\text{ km}^2$

• Park D: $1,250,000\text{ dam}^2$

In farming, special units are used. Match each International System measurement with its corresponding land area 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 forest fire has affected an area of the mountains. News reports indicate that $12\text{ km}^2$ and $45\text{ hm}^2$ of woodland have burned. To organise the reforestation, forestry technicians need to know the affected area in ares ($a$) and centiares ($ca$). Convert to both units.

A farmer owns a farm of $3\text{ ha}$, $5\text{ a}$ and $25\text{ ca}$. He decides to sell part of his land for the construction of a road. The part sold measures exactly $4,200\text{ m}^2$. What area of the farm, expressed in compound form (hectares, ares and centiares), does the farmer have left?

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

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

We want to replace the floor of a kitchen that is rectangular in 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 entire floor?

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

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 $\text{cm}^2$.

On a scale plan of a shopping center, the main corridor is represented by a rectangle with an area of $450\text{ cm}^2$. If we know that in reality this corridor 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?

The council has allocated land for school urban allotments with 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 vegetables per year and the average market price of the vegetables is $0.75 \text{ \text{RD\$}\ /kg}$, calculate the total value of the production of the entire land in one harvest.

For the construction of a new shopping center, a rectangular building lot measuring $2.4 \text{ hm}$ long and $150 \text{ m}$ wide has been fenced off. The municipality requires $25 \%$ of the total area to be allocated to green spaces and another $15 \%$ to parking lots. If the remainder is divided into store units with an average area of $120 \text{ m}^2$, how many store units can be built in total?

An artist wants to cover the side facade of a building with square solar panels measuring $50 \text{ cm}$ on each side. 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 deducted. Calculate the total number of solar panels he needs to buy to cover all the available area of the facade.

As part of a reforestation plan following a wildfire, work will be carried out over an area of $14 \text{ ha}, 5 \text{ a}$ and $20 \text{ ca}$. The 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 $\text{RD\$}\ 4.80$ and labor costs $\text{RD\$}\ 250$ per square decameter worked, what will be the total budget required 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, he adds four smaller squares whose sides are half the length of the central square's side. Express the total area of the logo in square millimeters and in square decimeters using only simple form.

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 park has an irregular shape that occupies $480 \text{ cm}^2$ on the map, calculate its real area in hectares, ares and centiares (compound form). If a fire destroys $0.4 \text{ km}^2$ of the park, 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 $\text{RD\$}\ 2\,700$. In addition to the cost of the material, the installation company charges $\text{RD\$}\ 1\,080$ per square meter laid. How much is the total bill if $5 \%$ more material than needed is bought to make up for what is wasted in cuts and breakage?

Calculate the total area of the following composite figure made of metal parts. The main part is a rectangle $0.8 \text{ m}$ by $15 \text{ cm}$, to which square tabs measuring $25 \text{ mm}$ on each side have been welded at each of its four vertices. In addition, a circular hole with an area of $450 \text{ mm}^2$ has been drilled in the center. Express the final result in square centimeters rounded to the nearest whole number.