Question

PQRS is a rhombus, SPO =35 ∠ ° , OS= 6 cm

a. Measure of POS is....... ∠

b. Find the area of the rhombus

( sin 35 = 0.57, cos 35=0.82,tan 35=0.70 )​

Answer 1

Answer:

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Answer 2

Answer:

(a) ∠POS = 90°

(b) Area of Rhombus PQRS = 102.84 sq cm.

Step-by-step explanation:

(a) From the properties of rhombus we know that, the diagonals of rhombus bisects each other at right angles.

$\therefore$ ∠POS = 90°

(b) Area of Rhombus = $\frac{1}{2} \times product\ of\ diagonals$

∠SPO = 35° and OS = 6 cm (Given)

$SQ=2OS$

$\therefore SQ = 2\times6=12\ cm$

From figure,

tan35° = $\frac{OS}{PO}$= $\frac{6}{PO}$

$0.70=\frac{6}{PO} \\PO=\frac{6}{0.70} \\PO=8.57\ cm$

$PR=2PO\\PR=2\times8.57=17.14\ cm$

Now,

Area of Rhombus PQRS = $\frac{1}{2} \times SQ\times PR$

$=\frac{1}{2} \times 12\times 17.14\\=102.84\ sq\ cm$

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