Heron S Formula(9th Grade > Mathematics ) Questions and answers for exam Preparation

9th Grade > Mathematics

HERON S FORMULA MCQs

Total Questions : 51 | Page 6 of 6 pages

Question 51.

Which of the following are correct regarding the given figure?

The area of a parallelogram is $120 c m^{2}$
The area of a parallelogram is $180 c m^{2}$
The length of the altitude is $15 c m$
The length of the altitude is $30 c m$

Discuss Question

Answer: Option B. -> The area of a parallelogram is

180 c m^{2}

:
B and C

For $△ B C D$ ,
$s = \frac{25 + 17 + 12}{2} = 27$
Using Heron's formula,
$A = \sqrt{27 (27 - 25) (27 - 17) (27 - 12)}$
$= \sqrt{27 \times 2 \times 10 \times 15}$
$= \sqrt{3 \times 3 \times 3 \times 2 \times 2 \times 5 \times 3 \times 5}$
$= 3 \times 3 \times 2 \times 5$
$= 90 c m^{2}$
The parallelogram can also be divided into 2 triangles by diagonal AC, as shown below, the area of each triangle being $= 90 c m^{2}$ .
Area of parallelogram $= 90 \times 2 = 180 c m^{2}$

In, $△ A C D$
Area of $△ ACD = \frac{1}{2} \times base \times Altitude$
$90 = \frac{1}{2} \times 12 \times Altitude$
$\Rightarrow Altitude = 15 c m$