The Perimeter and the Area of Quadrilaterals

By moving parts of the original quadrilateral, we can deduce the polygon has an area of |5\ \text{units}^2.|

To score a run in baseball, the player at bat must run to each base before finally returning to home plate. If a batter hits a homerun, the player can run the entire distance safely.

How far does a batter who hits a homerun have to travel before reaching home plate?

||\begin{align}A_\text{square}&=\color{#3a9a38}s\times \color{#3a9a38}s\\
&=\color{#3a9a38}s^2\end{align}||
where
​​|\color{#3a9a38}s:\text{side}​​|

A homeowner wants to know the surface area of his house’s floor because he plans to install hardwood.

Does he have enough money with a budget of |\ $1\ 000| if the material desired costs
|\ $9.95/\text{m}^2?|

To install a border around his rectangular garden, Julian decides to install cement borders.

What is the cost of the installation if Julian knows a cement block of |90\ \text{cm}| in length costs |\$ 8.95?|

||A_\text{rectangle}=\color{#3b87cd}b\times\color{#ec0000}h||
where
|\color{#3b87cd}b:\text{base}|
|\color{#ec0000}h:\text{height}|

To change the decor of a room, Suzy decides to paint one of the rectangular walls sky blue.

How much will the change cost her if a can of paint is sold for |\ $39.95,| and one can of paint covers an area of |20\ \text{m}^2?| She must also apply 3 coats of paint.

Amélie runs in a park along a path that from a bird’s eye view forms a parallelogram. Her average running speed is |6\ \text{min/km}.| If she starts in front of the big tree and ends at the same spot, how long does her run last?

||A_\text{parallelogram}=\color{#3b87cd}b\times \color{#ec0000}h||
where
|\color{#3b87cd}b:\text{base}|
|\color{#ec0000}h: \text{height}|

What is the area of the following parallelogram?

Which one of the following trapezoids has the largest perimeter?

||A_\text{trapezoid}=\dfrac{(\color{#3a9a38}{B}+\color{#3b87cd}b)\times\color{#ec0000}h}{2}||

where
|\color{#3a9a38}B:\text{large base}|
|\color{#3b87cd}b:\text{small base}|
|\color{#ec0000}h:\text{height}|

What is the area of the following trapezoid?

What is the perimeter of the following rhombus?

||A_\text{rhombus}=\dfrac{\color{#3b87cd}D\times\color{#ec0000}d}{2}||

where
|\color{#ec0000}d:\text{small diagonal}|
|\color{#3b87cd}D:\text{large diagonal}|

Theo has lost a card from his favorite deck of cards. It was the 7 of diamonds. Since he has a white card and some red paint, he decides to make a new card to replace it. The diamonds he paints are rhombi, all the same size. Given that one milliliter covers about |180\ \text{mm}^2,| how much paint will he need?

To protect the edges of a new kite, we want to buy plastic trim.

What is the total cost of the project if the material sells for |$1.95| per |10\ \text{cm?}|

||A_\text{kite}=\dfrac{\color{#ec0000}D\times \color{#3b87cd}d}{2}||

where
|\color{#ec0000}D:\text{large diagonal}|
|\color{#3b87cd}d:\text{small diagonal}|

The area formula of a kite is related to the rectangle's area formula. To understand where the formula comes from, refer to the proof of the formula for the area of a rhombus.

With changing weather conditions, a kite needs a new layer of water repellent for its surface so water won’t damage it.

Assuming that both sides of the kite must be treated, how much product should be purchased if |10\ \text{mL}| can cover an area of |1\ \text{dm}^2?|