Perimeters and areas of polygons

Calculate the perimetre and area of the rectangle in the diagram, with a base of $12$ cm and a height of $7$ cm.

A rectangular billboard has an area of $48\ \text{m}^2$ and its base measures $8$ m.

1. a) What is its height?
2. b) What is its perimetre?
3. c) If the billboard had the same area but a square shape, would that be possible? Reason your answer.

A football pitch measures $105$ m long and $68$ m wide.

1. a) Calculate its area in $\text{m}^2$.
2. b) Express the area in hectares. Remember that $1\ \text{ha} = 10.000\ \text{m}^2$.
3. c) Approximately how many football pitches like this one would fit inside a nature reserve of $1\ \text{km}^2$?

Calculate the area of the triangle in the diagram, with a base of $10$ m and a height of $6$ m.

A triangular billboard has a base of $4$ m and a height of $3$ m.

1. a) What is its area?
2. b) If the poster is printed on both sides, what total surface area needs to be printed?

To calculate the area of a triangle with base $12$ cm and height $7$ cm, a student calculated $12 \cdot 7 = 84$ and answered: "the area is $84\ \text{cm}^2$".

1. a) Explain what mistake they made.
2. b) Calculate the correct area.
3. c) The same student calculates the area of a rhombus with diagonals $10$ cm and $6$ cm and gets $60\ \text{cm}^2$. Do they make the same mistake again? Correct it.

The rhomboid in the diagram has a base of $9$ cm and a height of $5$ cm.

1. a) Calculate its area.
2. b) If the sloping side of the rhomboid measures $6$ cm, calculate its perimetre as well.

Calculate the area of the trapezium in the diagram, whose bases measure $14$ m and $8$ m and its height $6$ m.

The area of a trapezium is $84\ \text{m}^2$, its height is $7$ m and the longer base is $16$ m.

1. a) Substitute the data into the area formula of a trapezium, $A = \frac{(B + b) \cdot h}{2}$, and set up the corresponding equation.
2. b) Solve the equation and calculate the length of the shorter base.
3. c) Check your result by verifying that the area comes out to $84\ \text{m}^2$.

Calculate the area of the rhombus in the diagram, whose diagonals measure $16$ cm and $10$ cm.

The diagonals of a rhombus measure $20$ cm and $14$ cm.

1. a) Calculate its area.
2. b) If we cut the rhombus along its two diagonals, it is divided into $4$ identical right-angled triangles. What are the base and height of each of these triangles?
3. c) Calculate the area of one of these triangles and check that the four areas sum to the area of the rhombus.

The regular hexagon in the diagram has a side length of $6$ cm and its apothem measures $5,2$ cm.

1. a) Calculate its perimetre.
2. b) Calculate its area using the formula $A = \frac{P \cdot a}{2}$, where $P$ is the perimetre and $a$ is the apothem.