Area of a Triangle for an Equilateral Triangle

Q.

If the length of a median of an equilateral triangle is x cm, then its area is

1. $\frac{x^2}{2}$

2. $\frac{\sqrt{3}}{2}{x}^2$

3. $\frac{x^2}{\sqrt{3}}$

4. $x^2$

Q.

Find the area of an equilateral triangle having each side 4 cm.

Q.

Find the area of an equilateral triangle having altitude h cm.

Q. The triangle formed by joining the mid-points of an equilateral triangle is triangle.

1. an equilateral
2. an isosceles
3. a scalene

Q.

How to calculate the percentage of marks?

Q.

If the area of an equilateral triangle is $9\sqrt{3}{cm}^2$. What is the length of the side of the triangle.

1. 8 cm

2. 9 cm

3. 6 cm

4. 18 cm

Q.

Find the area of an equilateral triangle having each side x cm.

Q.

Write the following fractions as percentages:

$\frac{17}{25}$

Q.

Find the area of the equilateral triangle if its side is $7cm.$

Q.

Assertion : Area of an equilateral triangle of side ${\mathrm{a}}^{}$ is $=\frac{\sqrt{3}}{4}{\mathrm{a}}^2$.
Reason : The height of an equilateral triangle of side $a$ is $=\frac{\sqrt{3}}{4}a$

Which of the following is correct?

1. $\mathrm{A}$ is true and $\mathrm{R}$ is false.

2. $A$ is false and $R$ is true.

3. Both $\mathrm{A}$ and $\mathrm{R}$ are true and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$.

4. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.

Q.

What 's' denotes in the Heron's formula area of triangle=$\sqrt{s(s-a)(s-b)(s-c)}$ ?

1. perimeter

2. semi perimeter

3. area of the triangle

4. area of half of the triangle

Q. Consider four triangles having sides $(5,12,9),(5,12,11),(5,12,13)$ and $(5,12,15)$. among these, the triangle having maximum area has sides.

1. $(5,12,9)$
2. $(5,12,11)$
3. $(5,12,13)$
4. $(5,12,15)$

Q.

Evaluate $40\%$ of $50$

Q.

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is $12\sqrt{2}cm$, then the area of the triangle is:

1. $24\sqrt{3}c{m}^2$

2. $48\sqrt{3}c{m}^2$

3. $64\sqrt{3}c{m}^2$

4. $24\sqrt{2}c{m}^2$

Q.

Find the area of figure.

Q. A square and an equilateral triangle have equal perimeters. Ifthe diagonal of the square is $6\sqrt{2}$ cm, then the area of the triangle is

1. $16\sqrt{3}c{m}^2$
2. $12\sqrt{2}c{m}^2$
3. $16\sqrt{2}c{m}^2$
4. $12\sqrt{3}c{m}^2$

Q. Find the percentage increase in the area of a triangle if its each side is doubled.

Q. Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42 cm.

Q. A square and an equilateral triangle triangle have equal perimeters. If the diagonal of the square is $12\sqrt{2}$ cm, then area of the triangle is

1. $12\sqrt{2}c{m}^2$
2. $24\sqrt{3}c{m}^2$
3. $48\sqrt{3}c{m}^2$
4. $64\sqrt{3}c{m}^2$

Q. If the area of an equilateral triangle is $25\sqrt{3}$ sq. cms, then find its side.

1. $10$ cm
2. $5$ cm
3. $5\sqrt{3}$ cm
4. $10\sqrt{3}$ cm

Q.

Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42 cm.

Q. The sides of an equilateral triangle are
(2a - b + 5), (a + b) and (2b - a + 2). What is the area of the triangle?

1. $\frac{\sqrt{3}}{4}\times a^2$
2. $\frac{\sqrt{3}}{4}\times 81$
3. $\frac{\sqrt{3}}{4}\times b^2$
4. $\frac{\sqrt{3}}{4}\times 49$

Q. A caution sign is shown in the given figure. Find the area to be painted in red (shaded in figure), in order to warn the people about the danger ahead. [Use $\sqrt{3}=1.732$]

1. $443.4c{m}^2$
2. $440.4c{m}^2$
3. $438.4c{m}^2$
4. $449.4c{m}^2$

Q. The side of an equilateral triangle is $20\sqrt{3}cm$. The numerical value of the radius of the circle circumscribing the triangle is:

1. $20cm$
2. $20\sqrt{3}cm$
3. $20\pi cm$
4. $\frac{20}{\pi }$

Q. If $\Delta$ is the area of a triangle with sides of lengths a, b, c, then

1. $\Delta \le \frac{1}{4}\sqrt{(a+b+c)abc}$
2. $\Delta =\frac{1}{4}\sqrt{(a+b+c)abc}$ if $a=b=c$
3. $\Delta \ge \frac{1}{4}\sqrt{(a+b+c)abc}$
4. $\Delta =\frac{1}{4}abc\sqrt{(a+b+c)}$

Q. If the area of an equilateral triangle is $36\sqrt{3}c{m}^2$, then the length of the side of the triangle is .

1. 12 $cm$
2. 24 $cm$
3. 6 $cm$

Q. Find the perimeter of an isosceles right triangle with each of its congruent as 7cm.

1. $7\sqrt{2}$ cm
2. $14$ cm
3. $(2+\sqrt{2})$ cm
4. $7(2+\sqrt{2})$ cm

Q.

Find the area of an equilateral triangle of side 10 cm.

1. $18\sqrt{3}c{m}^2$

2. $25\sqrt{3}c{m}^2$

3. $12\sqrt{3}c{m}^2$

4. $27\sqrt{3}c{m}^2$

Q.

The area of an equilateral triangle with side 12cm is $36\sqrt{3}cm$

1. True

2. False

Q.

A point O is taken inside an equilateral $\Delta ABC$. If $OM\perp AC$, $OL\perp BC$ and $ON\perp AB$ such that OL = 14 cm, OM = 10 cm and ON = 6 cm, find the area of $\Delta ABC$.

1. $100\sqrt{3}c{m}^2$

2. $300\sqrt{3}c{m}^2$

3. $250\sqrt{3}c{m}^2$

4. $200\sqrt{3}c{m}^2$