Question

A regular octagon divided into a rectangle and two similar trapezium.
UT =8 cm ,VS= 5.6 cm, WR = 19.2 ,PQ = 8cm.​

Answer 1

Answer:

The length of side RS of the rectangle is 8 cm.

The lengths of sides QS and SR of the two trapeziums are 13.2 cm and 6.4

Step-by-step explanation:

From the above question,

They have given :

A regular octagon divided into a rectangle and two similar trapezium.

UT =8 cm ,VS= 5.6 cm, WR = 19.2 ,PQ = 8cm.​

We know that UT = 8 cm and WR = 19.2 cm.

We also know that PQ = 8 cm.

Using the Pythagorean Theorem, we can calculate VS as follows:

VS^2 = UT^2 + WR^2

VS^2 = 64 + 361.44

VS = √425.44 = 20.54 cm

Now we can calculate the length of side RS of the rectangle:

RS = PQ + VS

RS = 8 + 20.54

RS = 28.54 cm

To calculate the lengths of sides QS and SR of the two trapeziums, we can use the formula:

QS + SR = 2 x RS

QS + SR = 2 x 28.54

QS + SR = 57.08 cm

To calculate the lengths of QS and SR separately, we can subtract RS from both sides:

QS + SR - RS = 57.08 - 28.54

QS = 28.54 cm

SR = 28.54 cm

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