Question

Can I get help finding the area of question 3 please

Answer 1

We need to find the area of the rhombus given the next information:

-It has a perimeter of 40 in

- One of the diagonals has la length of 12 in

Now, the area is given by

`A=(d_1\cdot d_2)/(2)`

We know that one diagonal is equal to 12 in, then we can find the other diagonal using:

`\begin{gathered} d_2=\sqrt[]{4a^2-(d_1)^2} \\ \text{Replacing} \\ d_2=\sqrt[]{4(10\ln )^2-(12\ln _{})^2} \\ d_2=\sqrt[]{4\cdot100\ln ^2-144\ln ^2_{}} \\ d_2=\sqrt[]{400\ln ^2-144\ln ^2} \\ d_2=\sqrt[]{256\ln ^2} \\ d_2=16in \end{gathered}`

Replace d2 on the area formula:

`\begin{gathered} A=(d_1\cdot d_2)/(2) \\ A=\frac{12_{}\ln \cdot16\ln _{}}{2} \\ A=(192\ln ^2)/(2) \\ A=96\ln ^2 \end{gathered}`

Hence, the area f the rhombus is 96 in².