Question

The following diagram shows a pentagonal field $A B C D E$ in which the lengths of $A F, F G, G H$ and $H D$ are $50$ m, $40$ m, $15$ m and $25$ m respectively and the lengths of perpendiculars $B F, C H$ and $E G$ are $50$ m, $25$ m and $60$ m respectively. Determine the area of the field.

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Accepted Answer

We can divide the field into three triangles and one trapezium.

Let $A, B, C$ be the three triangular regions and $D$ be the trapezoidal region.

Now, Area of $A$ = $\frac{1}{2} \times A D \times G E$ = $\frac{1}{2} \times (50 + 40 + 15 + 25) \times 60$

$\Rightarrow$ Area of $A$ = $3900$ sq.cm

Area of $B$ = $\frac{1}{2} \times A F \times B F$ = $\frac{1}{2} \times 50 \times 50$

$\Rightarrow$ Area of $B$ = $1250$ sq.cm

Area of $C$ = $\frac{1}{2} \times H D \times C H$ = $\frac{1}{2} \times 25 \times 25$

$\Rightarrow$ Area of $C$ = $312.5$ sq.cm

Area of $D = \frac{1}{2} \times (B F + C H) \times (F G + G H)$

= $\frac{1}{2} \times (50 + 25) \times (40 + 15)$ = $\frac{1}{2} \times 75 \times 55$

$\Rightarrow$ Area of $D$ = $2062.5$ sq.cm

Area of the figure = Area of $A$ +Area of $B$ +Area of $C$ +Area of $D$

= $3900 + 1250 + 312.5 + 2062.5$ = $7525$ sq.cm

R K Bansal Solutions for Exercise 1: EXERCISE

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

^{Find the largest area enclosed by the same wire when bent to form a rectangle of breadth $16$ m.}

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R K Bansal Solutions for Exercise 1: EXERCISE

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

Find the largest area enclosed by the same wire when bent to form a rectangle of breadth 16m.

Learn and Prepare for any exam you want !

^{Find the largest area enclosed by the same wire when bent to form a rectangle of breadth $16$ m.}