Quadrilateral questions and answers are provided here for students to understand the topic better. The quadrilateral is an important topic for students because these concepts are studied in more depth in higher education. Here, we have provided questions involving quadrilaterals and related formulas that students can simply solve. The problems framed here follow the CBSE and NCERT syllabus. Practising these questions can assist students in solving difficult questions and achieving higher exam scores. Learn more about quadrilaterals here.
The quadrilateral is one of the most common geometrical shapes we observe in everyday life. As a result, students must be taught about quadrilaterals. The questions in this section have been prepared, so that students can do well not only in academic exams but also in competitive exams.
| Definition: In Geometry, a quadrilateral is a closed shape formed by connecting four points, among which three points are non-collinear. A quadrilateral is made up of four sides, four angles, and four vertices. It’s important to note that the sum of a quadrilateral’s internal angles is always 360°. |
Go through the below quadrilaterals questions and understand the concept quickly.
Quadrilateral Questions with Solutions
Types of Quadrilaterals:
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1. A quadrilateral with four equal sides and four right angles is a ______.
Solution:
Answer: Square.
A square is one of the quadrilaterals with four equal sides and four right angles.
2. The sum of interior angles of a quadrilateral is ____.
Solution:
Answer: 360°
The quadrilateral is a four-sided polygon, and hence the sum of the interior angles of a quadrilateral is 360°. A quadrilateral may be square, rectangle, parallelogram, rhombus, trapezium or kite-shaped.
3. The three angles of a quadrilateral are 60°, 90°, 110°. Determine the fourth angle.
Solution:
We know that the sum of interior angles of a quadrilateral is 360°.
Given three angles are 60°, 90° and 110°.
Let the unknown angle be “x”.
By using the property of quadrilateral,
60° + 90° + 110° + x = 360°
260° + x = 360°
x = 360° – 260°
x = 100°.
Hence, the fourth angle of a quadrilateral is 100°.
Quadrilateral Formulas:
Also, read: Types of Quadrilaterals |
4. The two angles of a quadrilateral are 76° and 68°. If the other two angles are in the ratio of 5: 7, then find the measure of each of them.
Solution:
Given two angles are 76° and 68°.
Let the other two angles be 5x and 7x.
As we know, the sum of interior angles of a quadrilateral is 360°.
Therefore, 76°+68°+5x + 7x = 360°
144° + 12x = 360°
12x = 360° – 144°
12x = 216°
x = 216°/12
x = 18°
Hence, the other two angles are:
5x = 5(18)° = 90°
7x = 7(18°) = 126°.
5. The dimension of the rectangular field is 30 m and 50 m. Find its area.
Solution:
Given: Length = 50 m
Breadth = 30 m
As the field is in the shape of a rectangle,
Area = Length × Breadth square units
Area = 50 × 30 m2
Area = 1500 m2
Hence, the area of the rectangular field is 1500 m2.
6. ABCD is a quadrilateral, whose angles are ∠A = 5(a+2)°, ∠B = 2(2a+7)°, ∠C = 64°, ∠D = ∠C-8°. Determine the value of ∠A.
Solution:
Given that, ∠A = 5(a+2)°, ∠B = 2(2a+7)°, ∠C = 64°, ∠D = ∠C-8°
Hence, ∠D = 64° – 8°
∠D = 56°
As we know,
∠A+∠B+∠C+∠D = 360°
Now, substitute the values, we get
5(a+2)° + 2(2a+7)° + 64°+56° = 360°
5a°+10°+4a°+14° +64° +56° = 360°
9a° + 144° = 360°
9a° = 360° – 144°
9a° = 216°
a° = 216°/9
a° = 24°
Hence, the value of ∠A is:
∠A = 5(a+2)° = 5(24°+2°) = 5 (26°) = 130°
Therefore, ∠A = 130°.
7. The angles of a quadrilateral are in the ratio of 1: 2: 3: 4. Find the measure of each angle.
Solution:
Given angle ratio is 1: 2: 3: 4.
Let the four angles be 1x, 2x, 3x, 4x.
As we know, the sum of interior angles of a quadrilateral is 360°.
Hence, 1x+2x+3x+4x = 360°
10x = 360°
x = 36°
Hence, the measure of four angles are:
⇒ x = 36°
⇒ 2x = 2(36°) = 72°
⇒ 3x = 3(36°) = 108°
⇒ 4x = 4(36°) = 144°
Therefore, the angles of a quadrilateral are 36°, 72°, 108° and 144°.
8. The lengths of adjacent sides of a parallelogram are 3 cm and 4 cm. Find its perimeter.
Solution:
Given that the length of the adjacent side of a parallelogram = 3 cm and 4 cm.
That is, base = 3 cm and side = 4 cm.
The formula to calculate the perimeter of a parallelogram is P = 2 (Base + Side) units
P = 2 (3+4)
P = 2 (7) = 14 cm
Hence, the perimeter of a parallelogram is 14 cm.
9. The diagonals of a rhombus are 12 cm and 7.5 cm. Find the area of a rhombus.
Solution:
Given: Length of diagonal 1 = 12 cm
Length of diagonal 2 = 7.5 cm
We know that,
Area of a rhombus = (1/2) × Diagonal 1× Diagonal 2 square units
A = (½)×12×7.5
A = 6×7.5
A = 45 cm2
Hence, the area of a rhombus is 45 cm2.
10. A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.
Solution:
Let A, B, C and D be the four angles of a quadrilateral.
If A=B=C=75°, we have to find the angle D
As we know that A+B+C+D = 360°
Therefore, 75°+75°+75°+D = 360°
225°+D = 360°
D = 360° – 225°
D = 135°.
Hence, the measure of the fourth angle is 135°.
Practice Questions
- If one angle of a parallelogram is 30° less than twice the smallest angle, find the measure of each angle.
- The adjacent sides of a parallelogram are in the ratio of 4: 5 and its perimeter is 72 m. Find the side lengths of a parallelogram.
- In a quadrilateral ABCD, ∠D = 150°, and ∠A = ∠B = ∠C. Find the measure of ∠A, ∠B and ∠C.
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