9th Class Mathematics Heron's Formula Question Bank

done Herons Formula Total Questions - 25

• question_answer1)
  In the given figure, the area of the \[\Delta ABC\] is
  A)
  \[13.24\,c{{m}^{2}}\]              done clear
  B)
  \[~12.28\,c{{m}^{2}}\]          done clear
  C)
                     \[~11.32\,c{{m}^{2}}\]            done clear
  D)
         \[~15.37\,c{{m}^{2}}\]                        done clear
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• question_answer2)
  The difference between the semi-perimeter and the sides of a \[\Delta ABC\] are 8 cm, 7 cm and 5 cm respectively. The area of the triangle is____.
  A)
  \[20\sqrt{7}\,c{{m}^{2}}\]        done clear
  B)
  \[10\sqrt{14}\,c{{m}^{2}}\]      done clear
  C)
  \[20\sqrt{14}\,c{{m}^{2}}\]      done clear
  D)
  \[140\,c{{m}^{2}}\]     done clear
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• question_answer3)
  The perimeter of a triangle is 540 m and its sides are in the ratio 25 : 17 : 12. Find its area.
  A)
  \[~9100\,{{m}^{2~}}\]                       done clear
  B)
  \[~9000\,{{m}^{2}}\]  done clear
  C)
  \[~9200\,{{m}^{2}}\]              done clear
  D)
         \[~9500\,{{m}^{2}}\]  done clear
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• question_answer4)
  The perimeter of an isosceles triangle is 32 cm. The ratio of one of the equal sides to its base is 3 : 2. Find the area of the triangle.
  A)
  \[48\,c{{m}^{2}}\]                   done clear
  B)
  \[28\sqrt{3}\,c{{m}^{2}}\]        done clear
  C)
  \[32\sqrt{2}\,c{{m}^{2}}\]        done clear
  D)
         \[44\,c{{m}^{2}}\]       done clear
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• question_answer5)
  If each side of the rhombus is 40 m and its longer diagonal is 48 m, then the area of rhombus is____.
  A)
  \[~1536\,{{m}^{2}}\]                          done clear
  B)
  \[~1636\,{{m}^{2}}\]  done clear
  C)
  \[~1236\,{{m}^{2}}\]              done clear
  D)
         \[~1336\,{{m}^{2}}\]  done clear
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• question_answer6)
  A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
  A)
   15 cm                          done clear
  B)
   14 cm  done clear
  C)
   12 cm              done clear
  D)
          13 cm  done clear
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• question_answer7)
  The area of a parallelogram ABCD in which AB = 12 cm, BC = 9 cm and diagonal AC = 15 cm is k cm2. Find the value of \[\frac{k-100}{4}.\]
  A)
   3                                 done clear
  B)
   4                     done clear
  C)
   2                     done clear
  D)
          5         done clear
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• question_answer8)
  In the given parallelogram, find the length of the altitude from vertex A on the side DC.
  A)
   18cm                           done clear
  B)
          12cm   done clear
  C)
          15cm                           done clear
  D)
          25cm done clear
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• question_answer9)
  A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of ` 5 per \[c{{m}^{2}}.\]Find the cost of painting.
  A)
   ` 880                           done clear
  B)
          ` 1020 done clear
  C)
          ` 960                           done clear
  D)
          ` 980               done clear
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• question_answer10)
  The area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm is \[k\sqrt{30}\,c{{m}^{2}}.\] Find the value of k.
  A)
   8           done clear
  B)
          6                                 done clear
  C)
          7                                 done clear
  D)
          9 done clear
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• question_answer11)
  In the given figure, AABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of \[\Delta ABC\] is constructed. Find the height DF of the parallelogram.
  A)
   3 cm                            done clear
  B)
          6 cm                done clear
  C)
          4 cm                            done clear
  D)
          2 cm                            done clear
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• question_answer12)
  The sides of a triangle are 11 cm, 15 err, and 16 cm. The altitude to the largest side is____.
  A)
  \[30\sqrt{7}\,cm\]                       done clear
  B)
         \[\frac{15\sqrt{7}}{2}\,cm\]                    done clear
  C)
         \[\frac{15\sqrt{7}}{4}\,cm\]                    done clear
  D)
          \[30\,cm\]                     done clear
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• question_answer13)
  A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
  A)
  \[~196\,c{{m}^{2}}\]                          done clear
  B)
         \[~186\,c{{m}^{2}}\]              done clear
  C)
         \[~169\,c{{m}^{2}}\]                          done clear
  D)
         \[~199\,c{{m}^{2}}\]              done clear
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• question_answer14)
  Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of ` 7 per \[{{m}^{2}}.\]
  A)
   ` 9500                         done clear
  B)
          ` 11000                        done clear
  C)
          ` 10500                        done clear
  D)
          ` 12500 done clear
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• question_answer15)
  The base of an isosceles triangle measures 24 cm and its area is\[192\text{ }c{{m}^{2}}.\] Find its perimeter.
  A)
   64 cm                          done clear
  B)
          46 cm              done clear
  C)
          84 cm                          done clear
  D)
          54 cm done clear
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• question_answer16)
  Suman made a picture with some white paper and a single coloured paper as shown in figure. White paper is available at her home and free of cost. The cost of coloured paper used is at the rate of 10p per\[c{{m}^{2}}.\] Find the total cost of the coloured paper used. (Take\[\sqrt{3}=1.732\]and\[\sqrt{11}=3.31\])
  A)
   ` 14.92                        done clear
  B)
          ` 14                 done clear
  C)
          ` 16                             done clear
  D)
          ` 13 done clear
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• question_answer17)
  An umbrella is made by stiching 12 triangular pieces of cloth of two different coloured as shown in given figure. Each piece measuring 40 cm, 40 cm and 18 cm. How much cloth of each colour is required for the umbrella?
  A)
  \[2104.56\text{ }c{{m}^{2}},\text{ }2104.56\text{ }c{{m}^{2}}\] done clear
  B)
         \[4209.22\text{ }c{{m}^{2}},\,2104.56\text{ }c{{m}^{2}}\] done clear
  C)
         \[1204.61\text{ }c{{m}^{2}},\text{ }1204.61\text{ }c{{m}^{2}}\] done clear
  D)
         \[2014.61\text{ }c{{m}^{2}},1204.61\text{ }c{{m}^{2}}\] done clear
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• question_answer18)
  A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown below. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the total area of paper needed to make the hand fan.
  A)
  \[840\,c{{m}^{2}}\]                 done clear
  B)
         \[1680\,c{{m}^{2}}\]               done clear
  C)
         \[480\,c{{m}^{2}}\]                 done clear
  D)
         \[7844\,c{{m}^{2}}\]                           done clear
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• question_answer19)
  The perimeter of a field in the form of an equilateral triangle is 36 cm, then its area is given by
  A)
  \[98\sqrt{3}\,c{{m}^{2}}\]                    done clear
  B)
         \[8\sqrt{3}\,c{{m}^{2}}\]                     done clear
  C)
         \[42\sqrt{3}\,c{{m}^{2}}\]                    done clear
  D)
          \[36\sqrt{3}\,c{{m}^{2}}\]       done clear
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• question_answer20)
  Tanya joined four triangles of cardboard to create a mask of Joker as shown in the given figure. Find the total area of the mask. (Given\[\sqrt{2}=1.41,\sqrt{3}=1.73\]]
  A)
  \[59.86\,c{{m}^{2}}\]              done clear
  B)
         \[50\,c{{m}^{2}}\]                   done clear
  C)
         \[59\,c{{m}^{2}}\]                   done clear
  D)
         \[53\,c{{m}^{2}}\]   done clear
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• question_answer21)
  ABC is an equilateral triangle of side \[4\sqrt{3}\]cm. P, Q and R are mid-points of AB, CA and BC respectively. Find the area of triangle PQR is ____.
  A)
  \[3\sqrt{3}\,c{{m}^{2}}\]                     done clear
  B)
         \[2\sqrt{3}\,c{{m}^{2}}\]         done clear
  C)
         \[\frac{\sqrt{3}}{2}\,c{{m}^{2}}\]        done clear
  D)
          \[\frac{\sqrt{3}}{4}c{{m}^{2}}\]         done clear
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• question_answer22)
  A design is made on a rectangular tile of dimensions\[50\,cm\,\times \,70\,cm\]as shown in figure. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tile respectively.
  A)
  \[1632\,c{{m}^{2}},1886\,c{{m}^{2}}\] done clear
  B)
         \[1538\,c{{m}^{2}},1632\,c{{m}^{2}}\] done clear
  C)
         \[1632\,c{{m}^{2}},1868\,c{{m}^{2}}\] done clear
  D)
          \[1538\,c{{m}^{2}},1632\,c{{m}^{2}}\]   done clear
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• question_answer23)
  Right isosceles triangles are constructed on the sides of right angled \[\Delta ABC\] with sides 3, 4, 5 units, as shown. A capital letter indicates area of each triangle. Which one of the following is true?
  A)
   X+Z = Y+W done clear
  B)
          W + X = Z done clear
  C)
          Y + Z = X done clear
  D)
         \[X+W=\frac{1}{2}(Y+Z)\] done clear
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• question_answer24)
  State T for true and 'F' for false.

  (i) The lengths of the three sides of a triangular field are 40 m, 24 m and 32 m respectively. The area of the triangle is \[384\text{ }{{m}^{2}}.\]

  (ii) The area of a quadrilateral ABCD in which B = 3 cm, BC= 4 cm, CD =4 cm, DA = 5 cm and AC = 5 cm is \[18\text{ }c{{m}^{2}}.\]

  (iii) An advertisement board is in the form of an isosceles triangle with its sides equal to 12 m, 10 m and 10 m. The cost of painting it at ` 2.25 per \[{{m}^{2}}\]is \[18\text{ }c{{m}^{2}}.\]112.

  (iv) Heron's formula cannot be used to calculate area of quadrilaterals.

  A)

  	(i)	(ii)	(iii)	(iv)
  	T	F	F	T

  done clear
  B)
        

  	(i)	(ii)	(iii)	(iv)
  	F	T	F	F

  done clear
  C)
        

  	(i)	(ii)	(iii)	(iv)
  	T	F	T	F

  done clear
  D)
        

  	(i)	(ii)	(iii)	(iv)
  	T	F	F	F

  done clear
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• question_answer25)
  Find the area of quadrilateral ABCD in which AB = 9 cm, 6C = 40 cm, CD = 28 cm, DA = 15 cm and \[\angle ABC={{90}^{o}}.\]
  A)
  \[~300\,c{{m}^{2}}\]                          done clear
  B)
         \[~180\,c{{m}^{2}}\]              done clear
  C)
         \[~126\,c{{m}^{2}}\]              done clear
  D)
         \[306\,c{{m}^{2}}\] done clear
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