Heron's Formula

Q. How to find area of triangle on graph paper

Q.

Find the area of a triangle, two sides of which are 8 cm and 12 cm and the perimeter is 38 cm .

1. $16\sqrt{3}{\text{cm}}^2$

2. $64{\text{cm}}^2$

3. $\sqrt{1463}{\text{cm}}^2$

4. $24\sqrt{3}{\text{cm}}^2$

Q. Herons formula for area of triangle, A; semiperimeter, s and sides a, b, c is given by

1. A² = s(s-a)(s-b)(s-c)
2. A² = (s-a)(s-b)(s-c)
3. A = s(s-a)(s-b)(s-c)
4. A² = s(s-a-b-c)

Q.

Question 96

Find the area enclosed by the following figure:

Q.

Which of the following expressions would you use to find the area of a trapezium?

1. (1/2) x ( sum of parallel sides ) x height of trapezium

2. (1/2) x base x height

3. Product of base and height

4. (1/2) x (sum of non parallel sides ) x height of trapezium

Q.

If the sides of a triangular field measure $51m$, $37m$ and $20m$, then the cost of leveling it at $Rs.5$ per $m^2$ is $Rs.1540$.

1. True
2. False

Q. Find the area of ∆ABC using Heron’s formula. The vertices of the triangle are A(1, 0), B(4, 4) and C(7, 0).​

Q.

Suppose p denotes the perimeter of a triangle with sides a, b and c and s is the semi perimeter and r is the inradius. If A denotes the area of the triangle, select the statements that are true.

1. $\frac{\sqrt{p(p-2a)(p-2b)(p-2c)}}{A}$ = 4

2. $r=\frac{A}{s}$

3. $\frac{\sqrt{p(p-2a)(p-2b)(p-2c)}}{A}$ = 9

4. $r=\frac{5A}{s}$

Q.

Is the fomula or finding the area of an equipaequil triangle is √3/4 × (Side)²

Q. what is the area of equilateral triangle in term of length of altitude ?

Q.

The sides of a triangle are in the ratio $1:2:2$ and its perimeter is $500\text{m}$. Then, area of the triangle is:

1. 2500$\sqrt{15}{m}^2$

2. 100$\sqrt{15}{m}^2$

3. 200$\sqrt{15}{m}^2$

4. 800$\sqrt{15}{m}^2$

Q. In the Heron's formula $\sqrt{s(s-a)(s-b)(s-c)}$, 's' is called the semi-perimeter.

1. False
2. True

Q. A regular hexagon has a side 6 cm. Its area is:

1. $10\sqrt{2}c{m}^2$
2. $54\sqrt{3}c{m}^2$
3. $27\sqrt{3}c{m}^2$
4. $9\sqrt{2}c{m}^2$

Q.

The sides of a triangle are 35 cm, 54 cm and 61 cm. The length of its longest altitude is

1. $24\sqrt{5}cm$

2. $48\sqrt{5}cm$

3. $56\sqrt{5}cm$

4. $108cm$

Q. The semi-perimeter of a triangle of sides 4 cm, 8 cm, 6 cm is 18 cm.

1. True
2. False

Q. The sides of a triangle are 8 cm, 10 cm and 6 cm respectively. Area of this triangle is .

1. 24 $c{m}^2$
2. 12 $c{m}^2$
3. 10 $c{m}^2$

Q. A metal wire, when bent in the form of an equilateral triangle of largest area, encloses an area of $484\sqrt{3}c{m}^2$ . If the same wire is bent into the form of a circle of largest area, find the area of this circle.

1. $1386c{m}^2$
2. $1388c{m}^2$
3. $1286c{m}^2$
4. $1186c{m}^2$

Q. If the area of a rhombus-shaped box is $6\sqrt{7}{cm}^2$ and its one diagonal is $6cm$. Find the side of the rhombus.

Q. If the perimeter of an equilateral triangle is 60 cm, then its area is 1732 $c{m}^2$.

1. False
2. True

Q.

A triangle and a parallelogram have the same base and 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.

1. 14 cm

2. 10 cm

3. 16 cm

4. 12 cm