Question

In a rectangular field of dimensions 60 m x 50 m, a triangular park is constructed. If the dimensional
the park are 50 m, 45 m and 35 m, find the area of the remaining field.​

Answer 1

${\underline{\underline{\text{\bf{Concept of the question : }}}}}$

Here the question is given from Area and perimeter of Triangle and Quadrilaterals. The question implies that A Rectangular Field has dimensions means length and Breadth are 60 m & 50 m respectively. In the field triangular park is constructed of dimensions means length of all sides are 50 m, 45 m, 35m. We have asked to find Area of remaining field.

${\underline{\underline{\text{\bf{Assumption : }}}}}$

• Let a, b, c be the sides of the triangle.
• l be the length and b be the Breadth of the rectangle.

${\underline{\underline{\text{\bf{Given} : }}}}$

✵Rectangular Field has

• Length = 60 m
• Breadth = 50 m

✵Triangular Field has

• Side a = 50 m
• Side b = 45 m
• Side c = 35 m

${\underline{\underline{\text{\bf{To find} : }}}}$

• Area of the Remaining part between Rectangular field and Triangular park.

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${\underline{\underline{\text{\bf{Formula used} : }}}}$

✵ For finding area of rectangle

$\bull \: \: { \sf{ {Area = Length \times Breadth }}}$

✵ For finding Area of triangle

• For finding the Area of triangle we are needed to find by Herons Formula that is

${ \sf{ \bull{ \: Semiperimeter = \cfrac{a + b + c}{2} }}}$

${ \sf{ \bull \: \: {Area = \sqrt{ s(s - a)(s-b)(s-c)}}}}$

Here,

• s is Semiperimeter
• a, b, c are sides.

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${\underline{\underline{\text{\bf{Solution with explanation } : }}}}$

✪ Area of the Rectangular Field is :-

${ \sf{\longmapsto{ Area = Length \times Breadth }}}$

${ \sf{\longmapsto{ Area =60 \times 50}}}$

${ \boxed{ \bf{\longmapsto{ Area =3000 \: {m}^{2} }}}}$

✪ Area of the Triangular field is :-

Semiperimeter is :-

${ \longmapsto{ \sf{ \: Semiperimeter = \cfrac{a + b + c}{2} }}}$

${ \longmapsto{ \sf{ \: Semiperimeter = \cfrac{50+ 45 + 35}{2} }}}$

${ \longmapsto{ \sf{ \: Semiperimeter = \cfrac{130}{2} }}}$

${ \longmapsto { \underline{ \sf{ \: Semiperimeter = 65 \: m \: }}}}$

Area is :-

${ \longmapsto{ \sf{ \: \: {Area = \sqrt{ s(s - a)(s-b)(s-c)}}}}}$

${ \longmapsto{ \sf{ \: \: {Area = \sqrt{ 65(65 - 50)(65-45)(65-35)}}}}}$

${ \longmapsto{ \sf{ \: \: {Area = \sqrt{ 65(15)(20)(30)}}}}}$

${ \longmapsto{ \sf{ \: \: {Area = \sqrt{ (5 \times 13)(5 \times 3)(5 \times 4)(5 \times 6)}}}}}$

${ \longmapsto{ \sf{ \: \: {Area = 5 \times 5\sqrt{ ( 13)(3)( 4)(6)}}}}}$

${ \longmapsto{ \sf{ \: \: {Area = 5 \times 5\sqrt{ ( 13)(3)( 2 \times 2)(3 \times 2)}}}}}$

${ \longmapsto{ \sf{ \: \: {Area = 5 \times 5 \times 3 \times 2\sqrt{ ( 13)( 2)}}}}}$

${ \longmapsto{ \sf{ \: \: {Area = 150\sqrt{ 26}}}}}$

${ \longmapsto{ \sf{ \: \: {Area = 150 \times 5.09}}}}$

${ \boxed{ \longmapsto{ \bf{ \: \: {Area = 763.5 \: {m}^{2} }}}}}$

✺ Area of the Remaining part :-

⇒ Area = Area of Rectangular Field - Area of Triangular park

⇒ Area = 3000 m² - 763 .5 m²

${ \large{\underline{ \overline{ \boxed{ \bf{Area = 2236.5 \: {m}^{2} }}}}}}$

So, Area of Remaining Part is 2236.5 m².

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*Note :- Kindly see answer from web if there is not clear view.

Refer to diagram also for well understanding.