Question

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

image of rhombus mnop with diagonals mo and np, and sides labeled 22.4 in each

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 correction: 14.3*42.6=609.18, half is 304.59≈304.6? Wait wait 14.3×42.6: 14×42.6=596.4, 0.3×42.6=12.78, total=596.4+12.78=609.18, half=304.59≈304.6. Oh earlier miscalculation. Correct step3: Area=0.5×14.3×42.6=304.59≈304.6
Wait wait the figure shows sides 22.4 but diagonals are MO and NP given as 14.3 and 42.6. So correct 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: Compute area

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

Answer:

301.4