Here are the step-by-step solutions for each problem on the worksheet.
1. State whether each quadrilateral is a rhombus.
Rule: A rhombus is a four-sided shape where
all four sides are equal in length.
*
a) The sides are 16 ft, 16 ft, 16 ft, and 16 ft. Since all sides are the same length, this
is a rhombus.
*
b) The sides are 12 yd, 6 yd, 12 yd, and 6 yd. The sides are not all equal (some are 12 and some are 6). This is
not a rhombus.
*
c) The sides are 23 m, 17 m, 23 m, and 17 m. The sides are not all equal. This is
not a rhombus.
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2. Find the area of each rhombus given below.
Formula: $\text{Area} = \frac{\text{diagonal}_1 \times \text{diagonal}_2}{2}$
*
a) Diagonals are $AQ = 18\text{ m}$ and $PC = 10\text{ m}$.
* $\text{Calculation: } \frac{18 \times 10}{2} = \frac{180}{2} = 90$
*
Answer: $90\text{ m}^2$
*
b) Diagonals are $PR = 11\text{ yd}$ and $SQ = 13\text{ yd}$.
* $\text{Calculation: } \frac{11 \times 13}{2} = \frac{143}{2} = 71.5$
*
Answer: $71.5\text{ yd}^2$
*
c) Diagonals are $EG = 20\text{ cm}$ and $HF = 22\text{ cm}$.
* $\text{Calculation: } \frac{20 \times 22}{2} = \frac{440}{2} = 220$
*
Answer: $220\text{ cm}^2$
---
3. Find the measure of the unknown angle in each rhombus.
Rules to use:
1.
Opposite angles in a rhombus are equal.
2.
Consecutive angles (angles next to each other) add up to $180^\circ$.
3. The diagonals bisect the corner angles (cut them exactly in half).
*
a) Find $\angle CAB$:
* We know $\angle C = 45^\circ$. Because opposite angles are equal, $\angle A$ (the whole angle at the top left) is also $45^\circ$.
* The diagonal line cuts angle A in half.
* $\text{Calculation: } 45^\circ / 2 = 22.5^\circ$
*
Answer: $22.5^\circ$
*
b) Find $\angle YZW$:
* We are given $\angle X = 70^\circ$.
* Angle Z is opposite to Angle X, so they are equal.
*
Answer: $70^\circ$
*
c) Find $\angle FGH$:
* We are given $\angle E = 66^\circ$.
* Angle G is opposite to Angle E, so they are equal.
*
Answer: $66^\circ$
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Final Answer:
1. Is it a rhombus?
a) Yes
b) No
c) No
2. Area
a) $90\text{ m}^2$
b) $71.5\text{ yd}^2$
c) $220\text{ cm}^2$
3. Unknown Angles
a) $\angle CAB = 22.5^\circ$
b) $\angle YZW = 70^\circ$
c) $\angle FGH = 66^\circ$
Parent Tip: Review the logic above to help your child master the concept of area of rhombus worksheet.
