The perimeter of the given polygon will be 25.52. The correct option is A.
What is a polygon?
A polygon is a closed polygonal chain made up of a finite number of straight line segments and is a type of planar figure in geometry. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.
The perimeter is defined as the sum of all the sides of any shape. The perimeter will be calculated by adding all the sides of the given polygon.
By using the Pythagorean theorem find QU.
QU² = 8² + 3²
QU² = 64 + 9
QU² = 73
QU = √73
QU = 3√7
By using the Pythagorean theorem find TU.
TU² = 4² + 1²
TU² = 16 + 1
TU² = 17
TU = √17
By using the Pythagorean theorem find TS.
TS² = 3² + 2²
TS² = 9 + 4
TS² = 13
TS = √13
By using the Pythagorean theorem find SR.
SR² = 4² + 2²
SR² = 16 + 4
SR² = 20
SR = √20
SR = 2√5
By using the Pythagorean theorem find QR.
QR² = 5² + 2²
QR² = 25 + 4
QR² = 29
QR = √29
The perimeter will be calculated as below:-
QR + QU + TU + TS + SR = 3√7 + √17 + √13 + 2√5 + √29 ≈ 25.52
Therefore, the perimeter of the given polygon will be 25.52. The correct option is A.
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