南外几何讲解-简单.doc

南外冲刺课程几何几何周长问题1) The adjacent sides of the decagon（十边形） shown meet at right angles and all dimensions（尺寸） are in metres.What is the perimeter, in metres, of this decagon?2) An L-shaped path is 5m wide and has an area of 125m2. The perimeter, in metres, of the figure is?3) A square piece of paper is folded in half. The resulting rectangle has a perimeter of 18 cm. What is the area, in square centimetres, of the original square?4) The perimeter of the equilateral triangle PQR is 48 cm. What is the perimeter, in centimetres, of the parallelogram PSTU? 5) Nelly correctly measures three sides of a rectangle and gets a total of 88 cm. HerBrother. Raffy correctly measures three sides of the same rectangle and gets a total of80 cm. What is the perimeter of the rectangle, in cm?Four points P, Q, R and S are such that PQ = 10, QR = 30, RS = 15 and PS = m. If m is an integer and no three of these points lie on a straight line, what is the number of possible values of m?A shape is formed when a regular hexagon of side 9 cm has six regular hexagons of side 3 cm added to the outside of it with one at the centre of each side (two of the sides are shown).What is the perimeter, in centimetres, of the shape?等高6) In a right-angled triangle ACD, the area of shaded region is 10 cm2, as shown in the figure below. AD = 5 cm, AB = BC, DE = EC. Find the length of AB.7) In rectangle ABCD, AB = 12 and AD = 5. Points P, Q, R and S are all on diagonal AC, so that AP = PQ = QR = RS = SC. What is the total area of the shaded region?角8) In the diagram, the size of three angles are given. Find the value of x.9) In the diagram, PQRS is a square. The value of x is10) In the following figure, if CA = CE, what is the value of x?11) In triangle ABC, AP = AQ and BQ = BR. Determine angle PQR, in degrees.12) This sheriffs badge(司法徽章) has ten equal sides, five 60 angles and five equal reflex angles.The value of x is勾股定理13) The area of square ABCD is 64 and AX=BW=CZ=DY=2. What is the area of square WXYZ?14) A rectangle with a length of 60 and a width of 45 can be divided(分) into 2700 squares with a side length of 1. If you draw a diagonal(对角线)of the rectangle, how many squares does the diagonal go through?15) A 36 cm by 24 cm rectangle is drawn on 1 cm grid paper such that the 36 cm side contains 37 grid points and the 24 cm side contains 25 grid points. A diagonal of the rectangle is drawn. How many grid points lie on that diagonal?16) Mary has 62 square blue tiles and a number of square red tiles. All tiles are the same size. She makes a rectangle with red tiles inside and blue tiles on the perimeter. What is the largest number of red tiles she could have used?17) What percentage of the largest square is covered by the shaded square?18) Three rectangles are lined up horizontally as shown. The lengths of the rectangles are 2 cm, 4 cm and 8 cm respectively. The heights are 1 cm, 2 cm and 4 cm respectively. A straight line is drawn from the top right-hand corner of the largest rectangle to the bottom left-hand corner of the smallest rectangle. What is the area, in square centimetres, of the shaded region?19) The areas, in square centimetres, of three rectangles are given. What is the area, in square centimetres, of the shaded rectangle?20) What is the area, in square centimetres, of the shape marked out on the 1 cm grid below?圆（04年真题） 21) Which picture has the same shadow area(阴影面积) as the first picture?22) There is a square pool. The length of every side( 边长) is 10m. E is themidpoint of AB. There is a sheep tied(栓) to E. The rope(绳子) is 6m. What isthe largest area(最大面积) where the sheep can walk?(3)23) Look at the picture. The radius(半径) of the small circle is 25 cm and that of the big circle is 50 cm. The small circle goes around the outside of the big circle. Then how many times does the smaller circle spin(自身转了几圈)?24) As shown in the figure, the perimeter(周长) of the trapezoid(梯形) is five times the perimeter of the circle. If the circle goes around the trapezoid, do you know how many times does the circle spin?25) A giraffe lives in an area shaped in the form of a right-angled triangle. The base and the height of the triangle are 12 m and 16 m respectively. The area is surrounded by a fence. The giraffe can eat the grass outside the fence at a maximum distance of 2 m. What is the maximum area outside the fence, in which the grass can be eaten by the giraffe?26) In the diagram, there are two touching circles, each of radius 2 cm. An ant starts at point A and walks around the figure 8 path ABCDEFCGA in that order. The ant repeats the figure 8 walk, again and again. After the ant has walked a distance of 2005p cm it becomes tired and stops. The ant stops at a point in the path. What letter point is it?27) There are five circles with 3 different diameters. Some of the circles touch each other as shown in the figure below. If the total area of the unshaded parts is 20 cm2, find the total area of the shaded parts, in cm2.切割28) In a regular hexagon ABCDEF, two diagonals, FC and BD, intersect at G. What is the ratio of the area of BCG to that of quadrilateral FEDG?29) Let ABCDEF be a regular hexagon. O is the centre of the hexagon. M and N are the mid-points of DE and OB respectively. If the sum of areas of FNO and FME is 3 cm2, find the area of the hexagon.立体几何：30) The volume of the solid figure below is _A.12B.30C.35D.36E.40（05年真题）31) There is 480 milliliter(毫升) of drinks in the bottle. How many milliliters is the volume(容积) of the bottle?A.840 B.100 C.960 D.640 （09年真题）32) There is some water in a cylindrical container(圆柱体容器). If you put a ball into the water(the ball is completely submerged), the water will rise(升高) 2cm;If you put a cone(圆锥体) with a diameter of 1cm and a height of 4cm, the water will rise 1.5cm. What is the volume(体积) of the ball? (取3)33) Look at the picture. It is an unfolded cube (正方体展开图).If we fold it into a cube(立方体)again, which point(点) will overlap(与重叠) Point A？34) Look at the picture of the piled cubes (堆积的正方体). How many cubes cant you see?35) An 8 8 8 hollow cube is constructed from 1 1 1 cubes so that its six walls are 1 cube thick. The number of 1 1 1 cubes needed to make the hollow cube is？36) The big cube(正方体) of ABCDEFGH is made up of some small cubes. There are 21 small cubes on the diagonal lines (对角线) AG and BH. How many small cubes is the big cube made up(组成) of in all?37) There are 4 dice(骰子)stacked(堆叠)together. It is known the sum of the two numbers on two opposite(相对) faces is 7What is the sum of the numbers on the faces indicated by 1, 2, 3, 4, 5, 6, 7?38) As shown in the figure: a big cube is composed(组成) of many small cubes. A small cube is taken away from its vertex(顶点). How many cubes are left?39) A wooden rectangular bl