Question

given rt=14.3 and su=43, find the area of rhombus rstu. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Recall the formula for the area of a rhombus

The area of a rhombus is given by the formula \( A=\frac{1}{2}d_1d_2 \), where \( d_1 \) and \( d_2 \) are the lengths of the diagonals of the rhombus.

Step2: Identify the lengths of the diagonals

From the problem, we are given that \( RT = 14.3 \) and \( SU=43 \). These are the lengths of the two diagonals of the rhombus \( RSTU \), so \( d_1 = 14.3 \) and \( d_2=43 \).

Step3: Substitute the values into the formula

Substitute \( d_1 = 14.3 \) and \( d_2 = 43 \) into the formula \( A=\frac{1}{2}d_1d_2 \):
\[
A=\frac{1}{2}\times14.3\times43
\]

Step4: Calculate the product

First, calculate \( 14.3\times43 \):
\( 14.3\times43=(14 + 0.3)\times43=14\times43+0.3\times43 = 602+12.9 = 614.9 \)

Then, multiply by \( \frac{1}{2} \):
\( A=\frac{1}{2}\times614.9 = 307.45 \)

Step5: Round to the nearest tenth (if necessary)

The value \( 307.45 \) rounded to the nearest tenth is \( 307.5 \) (since the hundredth digit is 5, we round up the tenth digit).

Answer:

\( 307.5 \)