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Area of a rhombus worksheet. A rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length.

1.
Solve for the areas of rhombi and kites by decomposing these shapes into triangles,

Practice Set C

1. Which shape has the greater area?

a. The rhombus’s area is greater than the kite’s area.

b. The kite’s area is greater than the rhombus’s area.

c. The rhombus and the kite have equal areas.

d. It is not possible to determine which has the greater area.

2. What are the areas for the rhombus and kite? Explain how you solved for their areas.

Practice Set C

1. Which shape has the greater area?

a. The rhombus’s area is greater than the kite’s area.

b. The kite’s area is greater than the rhombus’s area.

c. The rhombus and the kite have equal areas.

d. It is not possible to determine which has the greater area.

2. What are the areas for the rhombus and kite? Explain how you solved for their areas.

2.
3. The formula used to solve for the area of a rhombus is below. Lines p and q represent the

diagonals. How does the formula relate to decomposing the rhombus into two triangles? You

may construct a rhombus to help you explain your reasoning.

4. The formula used to solve for the area of a kite is below. Lines p and q represent the

diagonals. How does the formula relate to decomposing the kite into two triangles? You may

construct a kite to help you explain your reasoning.

diagonals. How does the formula relate to decomposing the rhombus into two triangles? You

may construct a rhombus to help you explain your reasoning.

4. The formula used to solve for the area of a kite is below. Lines p and q represent the

diagonals. How does the formula relate to decomposing the kite into two triangles? You may

construct a kite to help you explain your reasoning.

3.
Solve for the areas of rhombi and kites by decomposing these shapes into triangles,

Practice Set C

Answer Key

1. Which shape has the greater area?

a. The rhombus’s area is greater than the kite’s area.

b. The kite’s area is greater than the rhombus’s area.

c. The rhombus and the kite have equal areas.

d. It is not possible to determine which has the greater area.

2. What are the areas for the rhombus and kite? Explain how you solved for their areas.

Practice Set C

Answer Key

1. Which shape has the greater area?

a. The rhombus’s area is greater than the kite’s area.

b. The kite’s area is greater than the rhombus’s area.

c. The rhombus and the kite have equal areas.

d. It is not possible to determine which has the greater area.

2. What are the areas for the rhombus and kite? Explain how you solved for their areas.

4.
3. The formula used to solve for the area of a rhombus is below. Lines p and q represent the

diagonals. How does the formula relate to decomposing the rhombus into two triangles? You

may construct a rhombus to help you explain your reasoning.

The base of the two triangles is represented by either diagonal p or q. The heights of both

triangles are equivalent in a rhombus, so together they would equal the length of whichever

diagonal was not designated as the base.

diagonals. How does the formula relate to decomposing the rhombus into two triangles? You

may construct a rhombus to help you explain your reasoning.

The base of the two triangles is represented by either diagonal p or q. The heights of both

triangles are equivalent in a rhombus, so together they would equal the length of whichever

diagonal was not designated as the base.

5.
To find the area of any triangle, you apply the formula A= (½)(Base x Height), which is the

same as (Base x Height)/2. Because line q represents the base and line p represents the

height, we know that we multiply them together and divide them by 2 to solve for the area of

the rhombus. Decomposing the rhombus into two triangles and solving for each of their areas

gives you a total area of 6 square meters. Applying the formula also gives you an area of 6

square meters.

4. The formula used to solve for the area of a kite is below. Lines p and q represent the

diagonals. How does the formula relate to decomposing the kite into two triangles? You may

construct a kite to help you explain your reasoning.

The sum of the heights of the two triangles can be represented by one of the diagonals, while

the base is represented by the other. When decomposed into two triangles, the two triangles

share the same base.

For any triangle, the area can be found by applying the area formula for triangles: A=(½)(Base

x Height), or A=(Base x Height)/2. Combining the heights into one measurement (diagonal p),

multiplying that measurement by the base (diagonal q) and dividing that product by 2 is the

same as applying the area formula for two different triangles.

Decomposing the kite into two triangles and solving for the sum of their areas gives you an

same as (Base x Height)/2. Because line q represents the base and line p represents the

height, we know that we multiply them together and divide them by 2 to solve for the area of

the rhombus. Decomposing the rhombus into two triangles and solving for each of their areas

gives you a total area of 6 square meters. Applying the formula also gives you an area of 6

square meters.

4. The formula used to solve for the area of a kite is below. Lines p and q represent the

diagonals. How does the formula relate to decomposing the kite into two triangles? You may

construct a kite to help you explain your reasoning.

The sum of the heights of the two triangles can be represented by one of the diagonals, while

the base is represented by the other. When decomposed into two triangles, the two triangles

share the same base.

For any triangle, the area can be found by applying the area formula for triangles: A=(½)(Base

x Height), or A=(Base x Height)/2. Combining the heights into one measurement (diagonal p),

multiplying that measurement by the base (diagonal q) and dividing that product by 2 is the

same as applying the area formula for two different triangles.

Decomposing the kite into two triangles and solving for the sum of their areas gives you an

6.
area of 12 square meters. Applying the area formula for kites also gives you 12 square