Question

he length of the side of a regular heptagon whose perimeter is 273 cm is ________________

a) 39 sq.cm
b) 39 cm
c) 49 sq.cm
d) 49 cm

Answer 1

Answer:

Each angle of regular heptagon = ( n-2)*180 /n

= 5* 180/7 = (900/7)°

Its half = (900/14)° = (450/7)° . . . . . .(1)

Each side of regular heptagon = p/7 unit

=> half of each side = (p/14) unit . . . . . . .(2)

By (1) & (2) we can calculate the height of small triangle , formed by joining 2 adjacent vertices to its centre. Then find the area of this small triangle & multiply it by 7.

Tan (450/7)° = height of small triangle/ (p/14)

=> h = (p/14)*tan(450/7)°

=> area of small triangle = 1/2 * p/7 * p/14 *tan(450/7)°

= (p/14²)* tan(450/7)°

=> area of regular heptagon = 7 * p/14² * tan(450/7)°

=> area( regular heptagon)

= (p/28*tan(450/7)° , where p is perimeter

Answer 2

$\underline{ \underline{ \Large \pmb{\sf { {Given:}} }} }$

• Perimeter of the heptagon = 273 cm

$\underline{ \underline{ \Large \pmb{\sf { {To \: calculate:}} }} }$

• Measure of the side.

$\underline{ \underline{ \Large \pmb{\sf { {Calculation:}} }} }$

✰ Here, as per the given question we are given that the perimeter of the heptagon is 273 cm. We have to find the measure each side of it. In order to find the length of the side of the regular heptagon, we'll form an algebraic equation and by solving that equation we'll find its side.

⠀⠀⠀⠀⠀_____________

As we know that,

$\bigstar \: \boxed{\sf { Perimeter_{(Heptagon)} = Side \times 7}}$

According to the question,

$\longrightarrow \sf { 273 \: cm = Side \times 7}$

» Transpose 7 from R.H.S to L.HS.

$\longrightarrow \sf { \dfrac{273 }{7}\: cm = Side}$

$\longrightarrow \boxed{\pmb{\rm \red { 39 \: cm = Side}}}$

Therefore, side of the heptagon is 39 cm.

${\underline {\boxed {\Large {\bf \purple { Option \: B !} }}}}$