Question

Which of the following are correct regarding the given figure?

• A. The area of a parallelogram is $120c{m}^2$
• B. The area of a parallelogram is $180c{m}^2$
• C. The length of the altitude is $15cm$
• D. The length of the altitude is $30cm$

Answer 1

Answer: (B), (C)

The correct options are
B The area of a parallelogram is $180c{m}^2$
C The length of the altitude is $15cm$

For $△BCD$,
$s=\frac{25+17+12}{2}=27$

Using Heron's formula,
$A=\sqrt{27(27-25)(27-17)(27-12)}$
$=90c{m}^2$

The parallelogram can also be divided into 2 triangles by diagonal AC, as shown below, the area of each triangle being $=90c{m}^2$.

Area of parallelogram $=90\times 2=180c{m}^2$


In, $△ACD$
Area of $△ACD=\frac{1}{2}\times base\times Altitude$
$90=\frac{1}{2}\times 12\times \text{Altitude}$
$\Rightarrow \text{Altitude}=15cm$