Question

For a plank, in the shape of parallelogram, the adjacent sides measure 12 cm and 17 cm and its one diagonal measures 25 cm. Find the cost of painting the plank at the rate of Rs.3 per cm^2​

Answer 1

Area of the plank = 16400 $cm^{2}$.

• A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height.
• A quadrilateral's interior angles add up to 360 degrees. Two pairs of parallel sides with equal lengths make up a parallelogram. Its area and perimeter are defined by the fact that it is a two-dimensional figure.

Now, the area of the plank can be divided by the diagonal into two equal triangles.

Now, the area of one triangle is,

Semi-perimeter = $\frac{12+17+25}{2} = 27$.

Now, area = $\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{27(27-12)(27-17)(27-25)} = 8100 cm^{2}$

Hence, area of the plank = 2 × 8100 = 16400 $cm^{2}$.

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