A ground is in the shape of parallelogram. The height of the parallelo

1.	A ground is in the shape of parallelogram. The height of the parallelogram is 14 metres and thecorresponding base is 8 metres longer than its height. Find the cost of levelling the ground at the rate of ` 15 per sq. m
Answer» Given: Height of the parallelogram (ground) = ${\bold{14\:m}}$ Base of the parallelogram (ground) = $\bold{(8+Height)\:m}$ Cost of levelling per m² = ${\bold {15/-}}$ To find: The cost of levelling the ground. Solution: To find the cost of levelling, FIRST we've to find the area of the ground. And it is given that the ground is in the SHAPE of a parallelogram, it's area will be the PRODUCT of its base and its height. Once we find the area, we can find the cost of levelling by multiplying the area with cost per m². So, now LET's do it !! $\normalsize{\boxed{\sf{Area\:of\: parallelogram=Base \times Height\:sq.units}}}$ Now substitute the measures given in the formula. $\implies{\sf{(8 + Height)\times 14}}$ $\implies{\sf{(8 + 14)\times 14}}$ $\implies{\sf{22 \times 14}}$ $\implies{\sf{308}}$ $\large\underline{\boxed{\rightarrow{\tt{Area\:of\:the\:ground=308\:{m}^{2}}}}}$ Now, let's find the cost of levelling the ground. $\normalsize{\boxed{\sf{Cost\:of\: levelling=Cost\:per\:{m}^{2}\times Area\:of\:the\:ground}}}$ $\implies{\sf{15\times308}}$ $\implies\underline{\sf{4620\:\:rupees}}$ ‎ Answer: The cost of levelling the ground will be $\large\underline{\boxed{\tt{\red{4620/-}}}}$ _______________________________________ Some important formulae for Area: $\normalsize{\sf{1)\:Triangle=\frac{1}{2}\times Base\times Height\:sq.units}}$ $\normalsize{\sf{2)\:Right-angled\: triangle=\frac{1}{2}ab\:sq.units}}$ $\normalsize{\sf{3)\:Quadrilateral=\frac{1}{2}\times d\times(h1+h2)\:sq.units}}$ $\normalsize{\sf{4)\:Trapezium=\frac{1}{2}h\times(a+b)\:sq.units}}$ $\normalsize{\sf{5)\:Rhombus=\frac{1}{2}\times d1\times d2\:sq.units}}$ $\normalsize{\sf{6)\:Rectangle=Length\times Breadth\:sq.units}}$ $\normalsize{\sf{7)\:Square={Side}^{2}\:sq.units}}$ $\normalsize{\sf{8)\:Circle=\pi{r}^{2}\:sq.units\:or\:\frac{1}{4}\pi{d}^{2}\:sq.units}}$ $\normalsize{\sf{9)\:Semi-circle=\frac{1}{2}\pi{r}^{2}\:sq.units}}$ $\normalsize{\sf{10)\:Quadrant\:of\:circle=\frac{1}{4}\pi{r}^{2}\:sq.units\:or\:\frac{\theta}{360°}\pi{r}^{2}\:sq.units}}$ $\normalsize{\sf{11)\:Scalene\: triangle=\sqrt{s(s - a)(s - b)(s - c)}\:sq.units}}$ $\normalsize{\sf{12)\:Equilateral\: triangle=\frac{\sqrt{3}}{4}{a}^{2}=\frac{1}{2}ah\:sq.units}}$ $\normalsize{\sf{13)\:Isosceles\: triangle=\frac{1}{2}\times b \times AD\:sq.units}}$

A ground is in the shape of parallelogram. The height of the parallelogram is 14 metres and thecorresponding base is 8 metres longer than its height. Find the cost of levelling the ground at the rate of ` 15 per sq. m

Answer»

Given:

Height of the parallelogram (ground) = ${\bold{14\:m}}$
Base of the parallelogram (ground) = $\bold{(8+Height)\:m}$
Cost of levelling per m² = ${\bold {15/-}}$

To find:

The cost of levelling the ground.

Solution:

To find the cost of levelling, FIRST we've to find the area of the ground. And it is given that the ground is in the SHAPE of a parallelogram, it's area will be the PRODUCT of its base and its height. Once we find the area, we can find the cost of levelling by multiplying the area with cost per m². So, now LET's do it !!

$\normalsize{\boxed{\sf{Area\:of\: parallelogram=Base \times Height\:sq.units}}}$

Now substitute the measures given in the formula.

$\implies{\sf{(8 + Height)\times 14}}$

$\implies{\sf{(8 + 14)\times 14}}$

$\implies{\sf{22 \times 14}}$

$\implies{\sf{308}}$

$\large\underline{\boxed{\rightarrow{\tt{Area\:of\:the\:ground=308\:{m}^{2}}}}}$

Now, let's find the cost of levelling the ground.

$\normalsize{\boxed{\sf{Cost\:of\: levelling=Cost\:per\:{m}^{2}\times Area\:of\:the\:ground}}}$

$\implies{\sf{15\times308}}$

$\implies\underline{\sf{4620\:\:rupees}}$

‎

Answer:

The cost of levelling the ground will be $\large\underline{\boxed{\tt{\red{4620/-}}}}$

_______________________________________

Some important formulae for Area:

$\normalsize{\sf{1)\:Triangle=\frac{1}{2}\times Base\times Height\:sq.units}}$

$\normalsize{\sf{2)\:Right-angled\: triangle=\frac{1}{2}ab\:sq.units}}$

$\normalsize{\sf{3)\:Quadrilateral=\frac{1}{2}\times d\times(h1+h2)\:sq.units}}$

$\normalsize{\sf{4)\:Trapezium=\frac{1}{2}h\times(a+b)\:sq.units}}$

$\normalsize{\sf{5)\:Rhombus=\frac{1}{2}\times d1\times d2\:sq.units}}$

$\normalsize{\sf{6)\:Rectangle=Length\times Breadth\:sq.units}}$

$\normalsize{\sf{7)\:Square={Side}^{2}\:sq.units}}$

$\normalsize{\sf{8)\:Circle=\pi{r}^{2}\:sq.units\:or\:\frac{1}{4}\pi{d}^{2}\:sq.units}}$

$\normalsize{\sf{9)\:Semi-circle=\frac{1}{2}\pi{r}^{2}\:sq.units}}$

$\normalsize{\sf{10)\:Quadrant\:of\:circle=\frac{1}{4}\pi{r}^{2}\:sq.units\:or\:\frac{\theta}{360°}\pi{r}^{2}\:sq.units}}$

$\normalsize{\sf{11)\:Scalene\: triangle=\sqrt{s(s - a)(s - b)(s - c)}\:sq.units}}$

$\normalsize{\sf{12)\:Equilateral\: triangle=\frac{\sqrt{3}}{4}{a}^{2}=\frac{1}{2}ah\:sq.units}}$

$\normalsize{\sf{13)\:Isosceles\: triangle=\frac{1}{2}\times b \times AD\:sq.units}}$