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Heron's Formula [NEW] Maths - Heron's Formula [NEW]

Gujarat Board (GSEB) - STD 9 - Maths (GSEB - English Medium). 118 questions in this chapter.

Question types

Heron's Formula [NEW] question types

118 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

118
Questions
8
Question groups
5
Question types
Sample Questions

Heron's Formula [NEW] questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q1 Mark
The sides of a triangle are 56 cm, 60 cm and 52 cm . Area of the triangle is
  • A
    $1322 cm^2$
  • B
    $1311 cm^2$
  • ✓
    $1344 cm^2$
  • D
    $1392 cm^2$

Answer: C.

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Q 2M.C.Q1 Mark
The sides of a triangle are 35 cm, 54 cm and 61 cm respectivery. The length of its longest altitude is
  • A
    $16 \sqrt{5} cm$
  • B
    $10 \sqrt{5} cm$
  • ✓
    $24 \sqrt{5} cm$
  • D
    28 cm

Answer: C.

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Q 3M.C.Q1 Mark
The perimeter of an equilateral triangle is 60 m . The area is
  • A
    $10 \sqrt{3} m^2$
  • B
    $15 \sqrt{3} m^2$
  • C
    $20 \sqrt{3} m^2$
  • ✓
    $100 \sqrt{3} m^2$

Answer: D.

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Q 4M.C.Q1 Mark
The length of each side of an equilateral triangle having an area of $9 \sqrt{3}cm^2$ is
  • A
    8 cm
  • B
    36 cm
  • C
    4 cm
  • ✓
    6 cm

Answer: D.

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Q 5M.C.Q1 Mark
The edges of a triangular board are 6 cm, 8 cm and 10 cm long. The cost of painting it at the rate of 9 paise per $cm ^2$ is
  • A
    ₹ 2
  • ✓
    ₹ 2.16
  • C
    ₹ 2.48
  • D
    ₹ 3

Answer: B.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 (A): The area of the isosceles triangle is $\frac{5}{4} \sqrt{11} cm^2$, if the perimeter is 11 cm and the base is 5 cm.
Statement-2 (R): The area of the equilateral triangle is $20 \sqrt{3} cm^2$ whose each side is 8 cm.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.

Answer: C.

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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 (A): The area of an isosceles triangle having base 24 cm and each of the equall sidies equal to 13 cm is $60 cm^2$.
Statement-2 (R): The area of an isosceles triangle with base $a$ and each equal side $b$ is $\frac{b}{4} \sqrt{4 a^2-b^2}.$
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2
  • B
    Statement-1 is true, Statement-2 is true: Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is true. Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.

Answer: C.

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Q 8Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 (A): The area of an isosceles triangle each of whose equal side is 13 cm and whose base is 24 cm is $60 cm^2$.
Statement-2 (R): The area of an isosceles triangle having base $a$ and each equal side $b$ is $\frac{b}{4} \sqrt{4 a^2-b^2}$
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.

Answer: C.

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Q 9Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 (A): The area of an equilateral triangle with each side a is $\Delta=\frac{\sqrt{3}}{4} a^2$ sq. units.
Statement-2 (R) : The area of a triangle with perimeter $2 s$ and sides a, b, c is given by $\Delta=\sqrt{s(s-a)(s-b)(s-c)}$.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.

Answer: A.

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Q 10Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 (A): The area of an equilateral triangle the length of whose each side is positive integer, is an irrational number.
Statement-2 (R): The area of an equilateral triangle having each side equal to a is $\frac{\sqrt{3}}{4} a^2$.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.

Answer: A.

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Q 254 Marks Questions4 Marks
The sides of a quadrilateral, taken in order as 5m, 12m, 14m, 15m respectively. The angle contained by first two sides is a right angle. Find its area.

 

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Q 264 Marks Questions4 Marks
The sides of a quadrilateral field, taken in order are 26m, 27m, 7m, 24m respectively. The angle contained by the last two sides is a right angle. Find its area.
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Q 29Case study (4 Marks)4 Marks
To beautify parks in a city, city municipal corporation decided to make triangular flower beds in parks as shown in Fig. The dimensions of a triangular flower bed are $75 m \times 80 m \times 85 m$. Based on this information answer the following questions:
Image
(i) If each triangular flower bed is to be fenced with two parallel wires one below the other than the length of the wire used is
(a) 120 m$\quad$(b) 240 m$\quad$(c) 260 m$\quad$(d) 480 m
(ii) The area of a flower bed is
(a) $300 \sqrt{42} m^2$$\quad$(b) $300 \sqrt{21} m^2$$\quad$(c) $600 \sqrt{21} m^2$$\quad$(d) $400 \sqrt{21} m^2$
(iii) If each triangular bed is an equilateral triangle of side 60 m, then its area is
(a) $900 \sqrt{3} m^2$$\quad$(b) $600 \sqrt{3} m^2$$\quad$(c) $1200 \sqrt{3} m^2$$\quad$(d) $400 \sqrt{3} m^2$
(iv) The area of an isosceles triangle with base 'a' and equal sides 'b' is given by
(a) $\frac{a}{4} \sqrt{4 b^2-a^2}$$\quad$(b) $\frac{b}{4} \sqrt{4 a^2-b^2}$$\quad$(c) $\frac{a}{2} \sqrt{2 b^2-a^2}$$\quad$(d) $\frac{b}{2} \sqrt{4 a^2-b^2}$
(v) If each triangular bed is in the form of an isosceles triangle with base 60 m and equal sides of length 40 m each, then area of a flower bed is
(a) $150 \sqrt{7} m^2$ $\quad$(b) $75 \sqrt{7} m^2$ $\quad$(c) $300 \sqrt{7} m^2$ $\quad$(d) $200 \sqrt{7} m^2$
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Q 30Case study (4 Marks)4 Marks
In India, sunlight is available in abundance. Solar panels harness this energy and convert it into electric power. Mr. Krishan installed a triangular shaped solar panel of size 9 m, 9 m and 10 m on the roof of his house. Assuming that in the peak sunlight hours, 1 m2 pannel produces 190 watts of electricity per hour, answer the related questions given below (Efficiency of the pannel and other factors are not accountable).
Image
(i) Perimeter of the solar panel is:
(a) 14 m $\quad$(b) 18 m $\quad$(c) 35 m $\quad$(d) 28 m
(ii) Are in $m ^2$ of the solar panel can be calculated using the formula
(a) $\sqrt{s(s-a)(s-b)(s-c)}$
(b) $\sqrt{(s-a)(s-b)(s-c)}$
(c) $\sqrt{s(a-s)(b-s)(c-s)}$
(d)$\frac{1}{2} \sqrt{s(s-a)(s-b)(s-c)}$
where s is the semi-perimeter of the panel and a, b and care its sides.
(iii) Area of solar panel is:
(a) $\sqrt{140}$ sq. m $\quad$(b) $10 \sqrt{14} sq \cdot m$
(c) $14 \sqrt{10}$ sq. m $\quad$(d) $100 \sqrt{14}$ sq. m
(iv) The whole panel will produce: [Take $\sqrt{14}=3.74$ ]
(a) $190 \times 3.7$ watts/hour
(b) $190 \times 37.4$ watts/hour
(c) $190 \times 374$ watts/hour
(d) $190 \times 0.374$ watts/hour
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