Embark on an enlightening journey into the realm of geometry with our meticulously crafted area of rhombus and kite worksheet. This educational resource empowers learners to delve into the intricacies of these fascinating shapes, unlocking their secrets through a series of engaging practice problems.
Delving into the fundamental concepts, we unravel the formulaic intricacies of rhombus and kite area calculations. With crystal-clear explanations and illustrative examples, we illuminate the relationship between their diagonals and area, empowering learners to conquer any geometrical challenge.
Area of Rhombus
A rhombus is a quadrilateral with four equal sides. The area of a rhombus is given by the formula:
Area = (1/2)
- d1
- d2
where d1 and d2 are the lengths of the diagonals of the rhombus.
Examples
- Find the area of a rhombus with diagonals of length 6 cm and 8 cm.
- Area = (1/2) – 6 cm – 8 cm = 24 cm 2
- Find the area of a rhombus with side length 5 cm and one diagonal of length 6 cm.
- Area = (1/2) – 6 cm – (2 – 5 cm) = 30 cm 2
Relationship between Diagonals and Area, Area of rhombus and kite worksheet
The diagonals of a rhombus are perpendicular bisectors of each other. This means that they divide the rhombus into four congruent right triangles. The area of each right triangle is given by:
Area = (1/2)
- d1
- d2
Therefore, the area of the rhombus is equal to the sum of the areas of the four right triangles.
Area of Kite
A kite is a quadrilateral with two pairs of adjacent sides that are equal. The area of a kite is given by the formula:
Area = (1/2)
- d1
- d2
where d1 and d2 are the lengths of the diagonals of the kite.
Examples
- Find the area of a kite with diagonals of length 6 cm and 8 cm.
- Area = (1/2) – 6 cm – 8 cm = 24 cm 2
- Find the area of a kite with side length 5 cm and one diagonal of length 6 cm.
- Area = (1/2) – 6 cm – (2 – 5 cm) = 30 cm 2
Relationship between Diagonals and Area, Area of rhombus and kite worksheet
The diagonals of a kite are not perpendicular to each other. However, they do bisect each other. This means that they divide the kite into two congruent triangles. The area of each triangle is given by:
Area = (1/2)
- d1
- d2
Therefore, the area of the kite is equal to the sum of the areas of the two triangles.
FAQ Corner: Area Of Rhombus And Kite Worksheet
What is the formula for calculating the area of a rhombus?
Area = (1/2) – d1 – d2, where d1 and d2 represent the lengths of the rhombus’s diagonals.
How can I determine the area of a kite?
Area = (1/2) – (d1 – d2), where d1 and d2 represent the lengths of the kite’s diagonals.
