Question

given mo=8.8 and np=26.1, find the area of rhombus mnop. 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 diagonals

In rhombus \( MNOP \), the diagonals are \( MO \) and \( NP \). We are given that \( MO = 8.8 \) and \( NP=26.1 \). Let \( d_1=MO = 8.8 \) and \( d_2 = NP=26.1 \).

Step3: Calculate the area

Substitute the values of \( d_1 \) and \( d_2 \) into the formula for the area of a rhombus:
\[
A=\frac{1}{2}\times d_1\times d_2=\frac{1}{2}\times8.8\times26.1
\]
First, calculate \( 8.8\times26.1 \):
\( 8.8\times26.1 = 8.8\times(26 + 0.1)=8.8\times26+8.8\times0.1 = 228.8+0.88 = 229.68 \)
Then, multiply by \( \frac{1}{2} \):
\( A=\frac{1}{2}\times229.68 = 114.84 \)

Answer:

\( 114.8 \) (rounded to the nearest tenth)