Find the area $A$ of a rhombus if side $a = 10 cm$ and diagonal $d_{2} = 4 cm$ .

Answer

$166 cm^{2}$

Explanation

STEP 1: find diagonal $d 1$

To find diagonal $d 1$ use formula:

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

After substituting $d_{2} = 4 cm$ and $a = 10 cm$ we have:

d_{1}^{2} + (4 cm)^{2} = 4 \cdot (10 cm)^{2}

d_{1}^{2} + 16 cm^{2} == 400 cm^{2}

d_{1}^{2} == 400 cm^{2} - 16 cm^{2}

d_{1}^{2} = 384 cm^{2}

d_{1} = 384 cm^{2}

d_{1} = 86 cm

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $d_{1} = 86 cm$ and $d_{2} = 4 cm$ we have:

A = \frac{8 6 cm \cdot 4 cm}{2}

A = \frac{32 6 cm ^{2}}{2}

A = 166 cm^{2}

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Find the area A of a rhombus if side a=10cm and diagonal d2​=4cm.

166​cm2

Find the area $A$ of a rhombus if side $a = 10 cm$ and diagonal $d_{2} = 4 cm$ .

$166 cm^{2}$