Question

In the given diagram, PQU is an equilateral Triangle, QR VU is a square and RSTU is a rhombus. Find the perimeter, in cm, of Figure PQRSTU.
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Answer 1

Step-by-step explanation:

Since PQU is an equilateral triangle.

∴PQ=PU=QU=4 cm

Also, QUVR is a square.

∴QU=UV=VR=QR=4 cm

Also, RUTS is a parallelogram

So, UT=SR=5 cm

RU=ST=4√2cm......diagonal=√2a

Now, required perimeter

=PU+UT+TS+SR+QR+PQ

=(4+4+5+5+4+4+4√2+4√2)cm=26+8√2 cm.

I hope this answer will help you....

Answer 2

Step-by-step explanation:

ꜱɪɴᴄᴇ ᴘQᴜ ɪꜱ ᴀɴ ᴇQᴜɪʟᴀᴛᴇʀᴀʟ ᴛʀɪᴀɴɢʟᴇ.

∴ᴘQ=ᴘᴜ=Qᴜ=4 ᴄᴍ

ᴀʟꜱᴏ, Qᴜᴠʀ ɪꜱ ᴀ ꜱQᴜᴀʀᴇ.

∴Qᴜ=ᴜᴠ=ᴠʀ=Qʀ=4 ᴄᴍ

ᴀʟꜱᴏ, ʀᴜᴛꜱ ɪꜱ ᴀ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ

ꜱᴏ, ᴜᴛ=ꜱʀ=5 ᴄᴍ

      ʀᴜ=ꜱᴛ=42ᴄᴍ......ᴅɪᴀɢᴏɴᴀʟ=2ᴀ

ɴᴏᴡ, ʀᴇQᴜɪʀᴇᴅ ᴘᴇʀɪᴍᴇᴛᴇʀ

=ᴘᴜ+ᴜᴛ+ᴛꜱ+ꜱʀ+Qʀ+ᴘQ

=(4+4+5+5+4+4+42+42)ᴄᴍ=26+82 ᴄᴍ.

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