Compound shapes and measurement problems

The figure shows a house formed by a rectangle $8$ m wide and $5$ m high, and a triangular roof $3$ m high.

1. a) Calculate the area of the rectangular part.
2. b) Calculate the area of the triangular roof.
3. c) What is the total area of the facade?

A giant letter 'T' for a photocall is formed by two rectangles: the top crossbar, $120$ cm long and $30$ cm high, and the vertical stem, $90$ cm high and $30$ cm wide, attached below and centred.

1. a) Calculate the total area of the sign.
2. b) If the material costs $8,50\ \text{€}$ per square metre, how much does the sign cost? First, express the area in $\text{m}^2$.

We want to paint a rectangular wall $5$ m wide and $2,5$ m high that has a window measuring $1,5$ m by $1,2$ m.

1. a) What surface area needs to be painted?
2. b) A tin of paint covers $10\ \text{m}^2$ and costs $24,90\ \text{€}$. How many tins are needed to apply two coats of paint? How much will they cost?

A small square of side length $2$ cm is cut out from a square piece of card of side length $8$ cm.

1. a) Calculate the area of the resulting shape. Does it depend on where the cut-out is made?
2. b) Calculate the perimetre of the resulting shape in each of these three cases: the cut-out is made at a corner, in the middle of a side and in the interior of the card (a hole).
3. c) A student claims: "If removing a piece from a shape decreases its area, the perimetre always decreases too." Is this true? Use your results from part b) to justify your answer.

The garden in the diagram is a rectangle measuring $12$ m by $8$ m with a circular swimming pool of radius $2$ m inside it.

1. a) Calculate the area of the whole garden.
2. b) Calculate the area of the pool (take $\pi \approx 3,14$).
3. c) What area of lawn remains?
4. d) How many metres of fencing are needed to enclose the entire garden?

The diagram shows a running track made up of two straight sections of $80$ m and two semicircles of radius $20$ m at the ends.

1. a) How long is each of the two curved sections? Remember that two identical semicircles form a complete circle (take $\pi \approx 3,14$).
2. b) Calculate the total length of one full lap of the track along its inside edge.
3. c) The lanes of the track are $1,22$ m wide. Does a runner cover the same distance running in the inside lane as in the outside lane? Reason your answer without doing calculations.

In the grid shown in the figure, each square represents $1\ \text{cm}^2$. The blue outline is the edge of a small lake.

1. a) Count the squares that lie entirely inside the lake.
2. b) Count those that the lake touches only in part.
3. c) Give an estimate of the area of the lake, explaining the criterion you used.

An ink blot has fallen onto grid paper with grid squares of $1\ \text{cm}^2$. Counting carefully, the blot completely covers $14$ squares and partially touches another $18$.

1. a) Between which two values is the area of the blot guaranteed to lie? Reason your answer.
2. b) Give a reasonable estimate of the area and explain the criteria you used.
3. c) What is the maximum possible error of your estimate?