M.M: 49 marks Date: 21/08/2011
Time: 1 hour 30 minutes
Q 1: Fill in the blanks (1 mark each question x 12 = 12 marks)
- Area of a triangle (normal formula) = __________________________.
- The formula given by Heron about the area of a triangle is also known as _____________ formula.
- Heron’s formula for finding area of a triangle is = ______________________________ (more than one character will come).
- Heron’s formula to find the area of a triangle should be used when it is not possible to find ____________ of the triangle.
- Area of a quadrilateral whose sides and one diagonal are given can be calculated by dividing the quadrilateral into ______ ______________ and using ___________ formula.
- Area of a parallelogram = _________________ (more than one word will come).
- Area of a trapezium = __________________________ (more than one word will come).
- The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is ___________.
- In Heron’s formula to calculate area of a triangle, semi perimeter, ____ = _________________.
- Area of a square with side “a” = ______.
- Perimeter of an equilateral triangle with each side “x” cm is _____ ____.
- With reference to Heron’s formula for finding area of a triangle, 2s = ___________________(more than one letter or word will come).
Q 2: An isosceles triangle has perimeter 40 cm and each of the equal sides is 15 cm. Find the area of the triangle. (3 marks)
Q 3: The perimeter of a triangular field is 675 m and its sides are in the ratio of 7:8:10. Find the area of the triangle. (3 marks)
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| Figure 1 |
Q 4: The triangular side walls of a flyover, shown in figure 1 have been used for advertisements. The sides of the walls are 82 m, 18 m and 80 m. The advertisements yield an earning of Rs. 4000/m2 per year. A company hired both walls for 4 months. How much rent did it pay? (5 marks)
Q 5: A field is in the shape of a trapezium whose parallel sides are 10 m and 25 m. The non parallel sides are 14 m and 13 m. Find the area of the field. (4 marks)
Q 6: Students of a school staged a rally for a cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA while other through AC, CD and DA (check figure 2). Then they cleaned the area enclosed within their lanes. If AB = 9 m, BC = 40 m, CD = 15 m, DA = 28 m and angle B = 900, which group cleaned more area and by how much? Find the total area cleaned by the students. (5 marks)
Q 7: Vimla has a triangular field with sides 240 m, 200 here shem, 360 m w grew wheat. In other triangular field with sides 240 m, 320 m, 400 m adjacent to the previous field, she wanted to grow potatoes and onions as shown in figure 3. She divided the field into two parts by joining the mid-point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area (in hectares) has been used for wheat, potatoes and onions? (1 hectare = 10,000 m2). (6 marks)
Q 8: A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 10 cm and sides 8 cm each is to be made of three different shades as shown in figure 4. How much paper of each shade had been used in it? (5 marks)
Q 9: Kiran made a picture of an aeroplane with coloured paper as shown in figure 5. Find the total area of the paper used. (6 marks)
