Question

given jl=10.1 and km=20.3, find the area of rhombus jklm. round your answer to the nearest tenth if necessary.
image of rhombus jklm with diagonals jl and km, and sides labeled 11.3 in each

Explanation:

Step1: Recall the formula for the area of a rhombus

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

Step2: Identify the diagonals

In rhombus \( JKLM \), the diagonals are \( JL \) and \( KM \). We are given \( JL = 10.1 \) and \( KM=20.3 \).

Step3: Substitute the values into the formula

Substitute \( d_1 = 10.1 \) and \( d_2=20.3 \) into the formula \( A=\frac{1}{2} \times d_1 \times d_2 \).
\[
A=\frac{1}{2} \times 10.1\times20.3
\]
First, calculate \( 10.1\times20.3 \): \( 10.1\times20.3 = (10 + 0.1)\times(20+0.3)=10\times20+10\times0.3 + 0.1\times20+0.1\times0.3=200 + 3+2 + 0.03 = 205.03 \)
Then, multiply by \( \frac{1}{2} \): \( A=\frac{1}{2}\times205.03 = 102.515 \)

Step4: Round to the nearest tenth

Rounding \( 102.515 \) to the nearest tenth gives \( 102.5 \) (since the hundredth digit is 1, which is less than 5, we round down the tenth digit).

Answer:

The area of rhombus \( JKLM \) is \( 102.5 \) (square units, assuming the given lengths are in appropriate units).