Quadrilateral Worksheet with Answers on Properties Formulas and Solved Examples
A quadrilateral is a two-dimensional enclosed figure with four sides and four angles. Quadrilaterals are also regarded as tetragons and quadrangles, at many a place. Typically, this geometric shape has three types, that are, convex, concave, and complex quadrilaterals. In a quadrilateral worksheet, students get to learn about these types of quadrilaterals in detail and the related concepts by solving sums.
Types of Quadrilateral
1. Convex Quadrilateral
In convex quadrilaterals, every interior angle is less than 180 degrees, and its diagonals exist inside the figure. The following are the examples of this type of quadrilaterals.
Trapezium
Parallelogram
Rhombus
Rectangle
Square
Oblong
Kite
Cyclic quadrilaterals
Bicentric quadrilaterals
2. Concave Quadrilaterals
Quadrilaterals with an interior angle of more than 180 degrees and an exterior diagonal are known as concave quadrilaterals. A prominent example of this type of quadrilaterals is a dart. It has a bilateral symmetry like kites, but one interior angle here is reflex. Referring to a quadrilateral review worksheet will help students get a better insight into the concepts of concave quadrilaterals with real-life examples.
3. Complex Quadrilaterals
A quadrilateral that has self-intersecting sides is known as a complex quadrilateral. Bow-tie or butterfly are prominent examples of this geometric shape.
In a mathematical approach, angles formed by these intersections are not part of this shape. This geometric shape has two acute interior angles and two reflex angels. Moreover, these two reflex angles appear outside of the shape, which can lead to certain confusions. However, they are still regarded as interior angles.
Furthermore, two line segments here cross and appear to create two additional interior angles; this geometric shape still has just four interior angles. Hence, these self-intersecting line segments do not add any other features to this shape.
Properties of Quadrilateral
The properties of quadrilaterals are as follows.
Four angles
Four vertices
Sum of all interior angles is 360 degree
Students can refer to the quadrilateral worksheet to learn and practice more about this topic.
What is Quadrilateral Worksheet?
A quadrilateral proofs worksheet is a set of questions and solutions that offer in-depth knowledge of the concept of geometry. Students can refer to these study materials to learn about important concepts, and theories related to this geometrical shape with pictures, and real-life examples.
Furthermore, these special quadrilaterals worksheets are prepared based on the curriculum and guidelines of CBSE. Hence, solving and practicing this worksheet will also help students to enhance their exam preparations. Also, these quadrilateral worksheet answers are highly convenient, offering students to find exercises and solutions as per their requirements.
Different Types of Quadrilateral Worksheet
There are different types of quadrilateral worksheets and here are some of the important ones.
1. Charts
The charts help students to get familiar with the concept of this geometric shape and its related concepts. With visually appealing charts, one can analyze and comprehend different concepts and their similarities and differences as well.
2. Angles
Angles in quadrilaterals worksheet will aid students in learning different properties of angles of quadrilaterals. It covers topics like how to measure indicated angles, and find out the angle of special quadrilaterals, etc.
3. Area
Understanding quadrilaterals class 8 worksheet will help students to practice and learn various properties of this geometrical figure. Also, they will learn how to find out various angle measures, side ratios of quadrilaterals, etc. in the whole number as well as in fractions.
4. Perimeter
Solving and practising these worksheets will help students to learn about the numerical questions on various types of quadrilaterals. They can calculate the perimeters of quadrilterals in decimals and integers and understand its congruent properties and solve various types of sums on quadrilaterals.
Apart from these, there is a dedicated worksheet for each type of a quadrilateral that can help students to understand this topic of geometry. It includes a separate worksheet on the sums of squares, rectangles, rhombus, parallelograms, trapeziums, etc.
Students can visit the official website of Vedantu or download the mobile app to find their required quadrilateral worksheets. Vedantu offers a variety of such study materials along with solutions helping students to understand this topic better. Moreover, the online classes and doubt clearing sessions available on this e-learning platform, can assists students for their doubts.
FAQs on Quadrilateral Worksheet Practice Questions on Properties and Types
1. What is a quadrilateral in maths?
A quadrilateral is a polygon with four sides, four vertices, and four angles. In basic geometry, quadrilaterals are closed 2D shapes formed by four line segments. The sum of all interior angles of any quadrilateral is always 360°. Common types include squares, rectangles, parallelograms, rhombuses, trapeziums, and kites.
2. What is the formula for the area of a quadrilateral?
The area of a quadrilateral depends on its type because there is no single formula for all quadrilaterals. Common formulas include:
- Square: Area = side × side
- Rectangle: Area = length × width
- Parallelogram: Area = base × height
- Rhombus: Area = (d₁ × d₂) ÷ 2
- Trapezium: Area = ½ × (sum of parallel sides) × height
3. What is the sum of interior angles of a quadrilateral?
The sum of the interior angles of any quadrilateral is 360°. This can be understood by dividing a quadrilateral into two triangles. Since each triangle has an angle sum of 180°, we get:
- 180° + 180° = 360°
4. What are the different types of quadrilaterals?
The main types of quadrilaterals are square, rectangle, parallelogram, rhombus, trapezium, and kite. Their key properties include:
- Square: All sides equal, all angles 90°
- Rectangle: Opposite sides equal, all angles 90°
- Parallelogram: Opposite sides parallel and equal
- Rhombus: All sides equal, opposite angles equal
- Trapezium: One pair of parallel sides
- Kite: Two pairs of adjacent equal sides
5. What is the difference between a square and a rectangle?
The main difference is that a square has all four sides equal, while a rectangle has only opposite sides equal. Both shapes have:
- Four right angles (90° each)
- Opposite sides parallel
6. How do you find the perimeter of a quadrilateral?
The perimeter of a quadrilateral is found by adding the lengths of all four sides. Formula:
- Perimeter = a + b + c + d
- Perimeter = 5 + 6 + 7 + 8 = 26 cm
7. What are the properties of a parallelogram?
A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Its key properties are:
- Opposite sides are equal and parallel
- Opposite angles are equal
- Consecutive angles add up to 180°
- Diagonals bisect each other
8. How do you calculate the area of a trapezium?
The area of a trapezium is calculated using the formula ½ × (a + b) × h, where a and b are the parallel sides and h is the height. Steps:
- Add the lengths of the parallel sides
- Multiply the sum by the height
- Divide the result by 2
- Area = ½ × (6 + 10) × 5 = ½ × 16 × 5 = 40 cm²
9. What is the difference between a rhombus and a kite?
The key difference is that a rhombus has all four sides equal, while a kite has only two pairs of adjacent equal sides. Additional differences:
- Rhombus: Opposite angles equal, diagonals bisect each other
- Kite: One pair of opposite angles equal, one diagonal bisects the other
10. Can you give an example of solving a quadrilateral angle problem?
To solve a quadrilateral angle problem, use the fact that the sum of interior angles is 360°. Example:
- Given angles: 80°, 95°, and 100°
- Add them: 80 + 95 + 100 = 275°
- Missing angle = 360° − 275° = 85°
