Download App

Heron’s Formula — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsHeron’s Formula1 Mark
MCQ
The area of an equilateral triangle having side length equal to $\sqrt\frac{3}{4}\text {cm}$ (using Heron’s formula) is:
  • A
    a. $\frac{2}{27}\text{sq.cm}$
  • B
    b. $\frac{2}{15}\text{sq.cm}$
  • ✓
    c. $3\sqrt\frac{3}{64}\text{sq.cm}$
  • D
    d.$\frac{3}{14}\text{sq.cm}$
✓

Answer

Correct option: C.
c. $3\sqrt\frac{3}{64}\text{sq.cm}$
c. $3\sqrt\frac{3}{64}\text{sq.cm}$Solution:
$\text{Here, } \text{a}=\text{b}=\text{c}\sqrt{\frac{3}{4}}$
$\text{Semiperimeter}=\frac{(\text{a}+\text{b}+\text{c})}{2} \frac{3\text{a}}{2}=3\sqrt{\frac{3}{8}\text{cm}}$
Using Heron’s formula,
$\text{A}=\sqrt{\text{s}\text(s-a)\text(s-b)\text(s-c)}$
$(\sqrt{3\sqrt{\frac{3}{8}}}) (3\sqrt{\frac{3}{8}}-\sqrt{\frac{3}{4}}) (3\sqrt{\frac{3}{8}}-\sqrt{\frac{3}{4}}) \sqrt{\frac{3}{4}}) $
$=3\sqrt{\frac{3}{64}}\text{s}\text{q}.\text{c}\text{m}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q" from Heron’s Formula→Heron’s Formula — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

$(x+1)$ is a factor of $x^n+1$ only if:
→
An angle in the semicircle is:
→
Write the correct answer in the following: Value of $(256)^{0.16} \times(256)^{0.09}$ is.
→
In $\triangle\text{ABC},\angle\text{B}=\angle\text{C}$ and ray $AX$ bisects the exterior angle $\angle\text{DAC}.$ If $\angle\text{DAX}=70^\circ$ then $\angle\text{ACB}=$
→
One angle is equal to three times its supplement. The measure of the angle is:
→
The cost of constructing a wall $8m$ long, $4m$ high and $20\ cm$ thick at the rate of $25\ per\ m^3$ is:
→
If $\text{x}-\frac{1}{\text{x}}=\frac{15}{4},$ than $\Big(\text{x}+\frac{1}{\text{x}}\Big)=$
→
The point which lies on $x-$axis at a distance of $3$ units in the positive direction of $x-$axis is:
→
The width of each of nine classes in a frequency distribution is $2.5$ and the lower class boundary of the lowest class 10.6. Then the upper class boundary of the highest class is:
→
We get a rhombus by joining the mid-points of the sides of a:
→