Find the area $A$ of a rhombus if side $a = 5 cm$ and diagonal $d_{1} = 6 cm$ .

Answer

$24 cm^{2}$

Explanation

STEP 1: find diagonal $d 2$

To find diagonal $d 2$ use formula:

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

After substituting $d_{1} = 6 cm$ and $a = 5 cm$ we have:

(6 cm)^{2} + d_{2}^{2} = 4 \cdot (5 cm)^{2}

36 cm^{2} + d_{2}^{2} = 100 cm^{2}

d_{2}^{2} = 100 cm^{2} - 36 cm^{2}

d_{2}^{2} = 64 cm^{2}

d_{2} = 64 cm^{2}

d_{2} = 8 cm

STEP 2: find area $A$

To find area $A$ use formula:

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

After substituting $d_{1} = 6 cm$ and $d_{2} = 8 cm$ we have:

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

A = \frac{48 cm ^{2}}{2}

A = 24 cm^{2}

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Find the area A of a rhombus if side a=5cm and diagonal d1​=6cm.

24cm2

Find the area $A$ of a rhombus if side $a = 5 cm$ and diagonal $d_{1} = 6 cm$ .

$24 cm^{2}$