Economista

| COLEGIO BILINGÜE BUCKINGHAM |
| MATEMATICAS 8° GEOMETRIA NIVEL MEDIO 2012-2013 II BIMESTRE |

1. The figure below represents the painted drawing of a hut. Measurements are in centimetres. XY is the axis of symmetry. Find the area painted in blue.



2. ABC is a triangle and thelength of sides are shown on the figure below.


(a) Find the perimeter of the triangle in terms of x.
(b) If the perimeter = 17 cm, find the value of x.
(c) Hence, find the length of each side of the triangle ABC.



3. ABCD is a rectangle of length 3x – 4 and width 14 – 2x(a) Find the perimeter of ABCD in terms of x.
(b) If the perimeter = 28 m, find the value of x.
(c) Hence, find the dimensions of the rectangle ABCD (that is, the value of its length and width).


4. A rectangle has its length double its width. The length of the side of a square is equal to the width of therectangle.
Let the side of the square be x.
(a) Find the perimeter of the square in terms of x.
(b) Find the perimeter of the rectangle in terms of x.
(c) Given that P is the sum of the perimeters of the square and the rectangle, express P in terms of x.
(d) If P = 30 cm, find the value of x.
(e) Hence, find thelengths of the sides of the square and the rectangle.


5. Four equilateral triangles are constructed on the four sides of a square as shown in the figure below.

Diagram not to scale
(a) Given that the perimeter of the shape above equals 24 cm, find the length of the side of the square.
(b)Hence, find the area of the square.


6. Over a period of six weeks, a book company packed 572 boxes with books. Each box was 25 cm by 15 cm by 20 cm and had to be taped as shown below. 5 cm overlap was required on each piece of tape.

Note: The blue represents the outline of the box and the black represents the tape(a) Find the total length of tape used.
(b) How many rolls of tape, each 75 m long, were required to tape the boxes?


7. The density of a liquid is 1.1 g/cm3. Find the radius of a cylinder required to hold 1,250 g of this liquid, if the height of the cylinder is 10 cm.


8. The solidsquare-based pyramid has height x m and volume 16,000 m3. Find the height, in terms of x, of the smaller (shaded) pyramid which has a volume of 2,000 m2.








9. A soft drink can, in a specific country, has the following dimensions.The can is made of aluminium, which is not biodegradable. Design a more environmentally friendly can in terms of the material needed and give its dimensions. Your can must have a 355 cm3 capacity.


10. Find the area of the following equilateral triangle.



11. There is a cube with 3 cmsides. Find its volume.


12. The graph of y = x – 2 defines a triangle with x and y axes. Find its area.


13. In the diagram below, the front of a two-floor building is shown.

Small squares represent windows. The building is 20 m × 6 m and each window is 1 m × 1 m. What...