Find the area $A$ of a rhombus if perimeter $P = 64 cm$ and diagonal $d_{2} = 85 cm$ .

Answer

$3255 cm^{2}$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

P = 4 \cdot a

After substituting $P = 64 cm$ we have:

64 cm = 4 \cdot a

a = \frac{64 cm}{4}

a = 16 cm

STEP 2: find diagonal $d 1$

To find diagonal $d 1$ use formula:

d_{1}^{2} + d_{2}^{2} = 4 \cdot a^{2}

After substituting $d_{2} = 85 cm$ and $a = 16 cm$ we have:

d_{1}^{2} + (85 cm)^{2} = 4 \cdot (16 cm)^{2}

d_{1}^{2} + 320 cm^{2} == 1024 cm^{2}

d_{1}^{2} == 1024 cm^{2} - 320 cm^{2}

d_{1}^{2} = 704 cm^{2}

d_{1} = 704 cm^{2}

d_{1} = 811 cm

STEP 3: find area $A$

To find area $A$ use formula:

A = \frac{d _{1} \cdot d _{2}}{2}

After substituting $d_{1} = 811 cm$ and $d_{2} = 85 cm$ we have:

A = \frac{8 11 cm \cdot 8 5 cm}{2}

A = \frac{64 55 cm ^{2}}{2}

A = 3255 cm^{2}

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Find the area A of a rhombus if perimeter P=64cm and diagonal d2​=85​cm.

3255​cm2

Find the area $A$ of a rhombus if perimeter $P = 64 cm$ and diagonal $d_{2} = 85 cm$ .

$3255 cm^{2}$