Question

given mo=14.3 and np=42.6, find the area of rhombus mnop. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Recall area formula for rhombus

Area = $\frac{1}{2} \times d_1 \times d_2$ (where $d_1,d_2$ are diagonals)

Step2: Identify diagonals

$d_1=MO=14.3$, $d_2=NP=42.6$

Step3: Calculate area

Area = $\frac{1}{2} \times 14.3 \times 42.6 = 7.15 \times 42.6 = 304.59$? Wait, no—wait the figure shows NP is split? No, wait the problem says NP=42.6 directly. Wait 14.342.6=609.18, half is 304.59, rounded to nearest tenth is 304.6? Wait wait no, wait the figure has 22.4 sides but problem gives MO=14.3 and NP=42.6. Oh yes: $\frac{1}{2}×14.3×42.6 = (14.3×42.6)/2 = 609.18/2 = 304.59 ≈304.6$. Wait I made a mistake earlier. Correct calculation: 14.342.6= let's compute: 1442.6=596.4, 0.342.6=12.78, total=596.4+12.78=609.18. Half is 304.59≈304.6. Oh right, my initial step 3 had a miscalculation. So correct answer is 304.6.

Wait wait, let's redo step3 properly:

Step3: Compute area

Area = $\frac{1}{2}×14.3×42.6 = 304.59 ≈304.6$

Yes, that's right. So final answer is 304.6.

Step1: Use rhombus area formula

Area = $\frac{1}{2}d_1d_2$

Step2: Substitute diagonal values

$d_1=14.3$, $d_2=42.6$

Step3: Calculate and round

$\frac{1}{2}×14.3×42.6=304.59≈304.6$

Answer:

301.4