Question

5. Find the area of hexagon park ABCDEF as per dimensions given herewith ​

Answer 1

• Area of hexagon ABCDEF is 340 cm².

Step-by-step explanation:

A Park ABCDEF is of hexagon shape.

Park is divided in two parts :

• First part ABCD is of trapezium shape because pair of Non equal sides are parallel.

• Second part ADEF is of square shape because it's three sides measure is 16 cm then fourth will be also 16 cm. And two angles are 90° thus it's other two angles will be also 90°.

________________________________

Trapezium ABCD :

Parallel sides of trapezium are BC and AD.

BC is of 8 cm.

ADFE is a square so AD is of 16 cm.

Height of trapezium ABCD is 7 cm.

Now,

$\boxed{\sf \bold{\star \: Area \: of \: trapezium = \dfrac{a + b}{2} \times h}}$

Where,

• a and b are parallel sides of trapezium and h is height of trapezium.

Put a, b and h in formula:

$\sf \longrightarrow \dfrac{8 + 16}{2} \times 7$

$\sf \longrightarrow \dfrac{24}{2} \times 7$

$\sf \longrightarrow \dfrac{168}{2}$

$\longrightarrow \pink{\boxed{\sf \bold{84}}\star}$

Area of ABCD is 84 cm²

_____________________________

Square ADEF:

Side is of 16 cm.

So,

$\boxed{\sf \bold{\star \: Area \: of \: square = Side \times Sides}}$

$\sf \longrightarrow 16 \times 16$

$\longrightarrow \purple{\boxed{\sf \bold{256}}\star}$

Area of ADEF is 256 cm².

_______________________________

Area of hexagon ABCDEF = Area of trapezium ABCD + Area of square ADEF.

$\sf \longrightarrow 256 - 84$

$\longrightarrow \red{\boxed{\sf \bold{340}}\star}$

Therefore,

Area of hexagon ABCDEF is 340 cm².

Answer 2

$\rule{200}4$

${ \frak { \underline \pink {\qquad Given\: : \qquad }}} \:$

• A hexagon park maded with joining square and trapezium.

• Side of square is 16 cm , parallel sides of trapezium are 8 cm and 16 cm and height of trapezium is 7 cm.

${ \frak { \underline \pink {\qquad To\:Find\: : \qquad }}} \:$

• Area of the park.

${ \frak { \underline \pink {\qquad Solution\: : \qquad }}} \:$

${\red\bigstar\:\underline{\boxed {\bold \green {Area_{(Square)}\:=\:(Side)^2}}}}$

${\red\bigstar\:\underline{\boxed {\bold \green {Area_{(Trapezium)}\:=\:\dfrac{1}{2}\:\times\:(Sum\:of\:parallel\:sides)\:\times\:height(h)}}}}$

${\pink\dag\large\tt\underline{\purple{Area\: of \:park \:= \:Area \:of \:square\: +\: Area \:of \:trapezium}}}\pink\dag$

$\dag\:\underline{\frak{Putting\:all\:values\:-}}$

$\longmapsto\:\sf{[(16)^2]\:+\:\bigg(\dfrac{1}{2}\:\times\:(8\:+\:16)\:\times\:7}\bigg)$

$\longmapsto\:\sf{(16\:\times\:16)\:+\:\bigg(\dfrac{1}{2}\:\times\:24\:\times\:7}\bigg)$

$\longmapsto\:\sf{(256)\:+\:\bigg(\dfrac{24}{2}\:\times\:7}\bigg)$

$\longmapsto\:\sf{(256)\:+\:\bigg(\dfrac{24\:\times\:7}{2}}\bigg)$

$\longmapsto\:\sf{(256)\:+\:\bigg(\dfrac{168}{2}}\bigg)$

$\longmapsto\:\sf{(256)\:+\:\bigg(\cancel{\dfrac{168}{2}}}\bigg)$

$\longmapsto\:\sf{(256)\:+\:(84)}$

$\longmapsto\:\sf{(256\:+\:84)}$

$\longmapsto\:\boxed{\boxed{\sf{340}}}\:\orange\bigstar$

$\underline{\boxed {\frak {\therefore \blue {Area_{(Hexagon\:Park)}\:\leadsto\:340\:cm^2}}}}\:\red\bigstar$

$\rule{200}4$