Area of a Triangle MCQ Quiz in मल्याळम - Objective Question with Answer for Area of a Triangle - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക
Last updated on Apr 1, 2025
Latest Area of a Triangle MCQ Objective Questions
Top Area of a Triangle MCQ Objective Questions
Area of a Triangle Question 1:
The area of the triangle whose vertices are (-2, a) (2, -6) and (5, 4) is 35 sq units then the value of 'a' is
Answer (Detailed Solution Below)
Area of a Triangle Question 1 Detailed Solution
Concept:
The area of a triangle with vertices
Calculations:
Vertices of triangle are (-2, a) (2, -6) and (5, 4)
Area = 35sq units
⇒
⇒
⇒
⇒
⇒ 70 = 58 + 3a
⇒ 12 = 3a
⇒
Hence, the correct option is 1) 4.
Area of a Triangle Question 2:
Find the possible value(s) of 't' if the area of the triangle formed by vertices (-2 , 0), (-2 , 8) and (t , 4) is 12 square units.
Answer (Detailed Solution Below)
Area of a Triangle Question 2 Detailed Solution
Concept:
Formula:
Area of triangle =
Calculation:
Given:
The area of the triangle formed by vertices (-2 , 0), (-2 , 8) and (t , 4) is 12 square units.
Area =
⇒ |-2(8 × 1 - 4 × 1) -0(-2 × 1 - t × 1) + 1(-2 × 4 - t × 8)| = 12 × 2
⇒ |-16 - 8t| = 24
⇒ |- 2 - t| = 3
⇒ - 2 - t = 3 or -2 - t = -3
⇒ t = -5, 1
So, the correct answer is option 2.
Area of a Triangle Question 3:
If the vertices of a triangle are (1, 2), (2, 5) and (4, 3) then the area of the triangle is :
Answer (Detailed Solution Below)
Area of a Triangle Question 3 Detailed Solution
Concept
The area of a triangle given its three vertices is
Explanation:
Hence Option(2) is the correct answer.
Area of a Triangle Question 4:
The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be
Answer (Detailed Solution Below)
Area of a Triangle Question 4 Detailed Solution
Concept:
Area of a triangle with vertices (x1, y1) , (x2, y2), (x3, y3) is given by
Area =
Explanation:
Given, the area of a triangle with vertices (-3, 0), (3, 0), and (0, k) is 9 square units.
∴ Area =
⇒ Area =
⇒ Area =
⇒ Area = 3k
The area of a triangle with vertices (-3, 0), (3, 0), and (0, k) is 9 square units.
∴ 3k = 9
⇒ k = 3
Area of a Triangle Question 5:
If the area of a triangle with the vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units, then the value of k is
Answer (Detailed Solution Below)
Area of a Triangle Question 5 Detailed Solution
Given;
The area of a triangle with the vertices (-3, 0), (3, 0) and (0, k) is 9 sq.
Concept:
Use concept of area of triangle using matrix.
Calculation:
The area of a triangle with the vertices (-3, 0), (3, 0) and (0, k) is 9 sq.
3k + 3k = 18
k = 3
Hence the option (1) is correct.
Area of a Triangle Question 6:
Find the possible value(s) of 't' if the area of the triangle formed by vertices (-2 , 0), (-2 , 8) and (t , 4) is 12 square units.
Answer (Detailed Solution Below)
Area of a Triangle Question 6 Detailed Solution
Concept:
Formula:
Area of triangle =
Calculation:
Given:
The area of the triangle formed by vertices (-2 , 0), (-2 , 8) and (t , 4) is 12 square units.
Area =
⇒ |-2(8 × 1 - 4 × 1) -0(-2 × 1 - t × 1) + 1(-2 × 4 - t × 8)| = 12 × 2
⇒ |-16 - 8t| = 24
⇒ |- 2 - t| = 3
⇒ - 2 - t = 3 or -2 - t = -3
⇒ t = -5, 1
So, the correct answer is option 2.
Area of a Triangle Question 7:
The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be
Answer (Detailed Solution Below)
Area of a Triangle Question 7 Detailed Solution
Concept:
Area of a triangle with vertices (x1, y1) , (x2, y2), (x3, y3) is given by
Area =
Explanation:
Given, the area of a triangle with vertices (-3, 0), (3, 0), and (0, k) is 9 square units.
∴ Area =
⇒ Area =
⇒ Area =
⇒ Area = 3k
The area of a triangle with vertices (-3, 0), (3, 0), and (0, k) is 9 square units.
∴ 3k = 9
⇒ k = 3
Area of a Triangle Question 8:
If the vertices of a triangle are (1, 2), (2, 5) and (4, 3) then the area of the triangle is :
Answer (Detailed Solution Below)
Area of a Triangle Question 8 Detailed Solution
Concept
The area of a triangle given its three vertices is
Explanation:
Hence Option(2) is the correct answer.
Area of a Triangle Question 9:
If the vertices of a triangle are (1, 2), (2, 5) and (4, 3) then the area of the triangle is :
Answer (Detailed Solution Below)
Area of a Triangle Question 9 Detailed Solution
Concept
The area of a triangle given its three vertices is
Explanation:
Hence Option(2) is the correct answer.
Area of a Triangle Question 10:
The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units, the value of k is
Answer (Detailed Solution Below)
Area of a Triangle Question 10 Detailed Solution
Concept:
- Area of a Triangle using Coordinates: The area of a triangle with vertices at (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by the formula:
- Area = (1/2) × |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
- This formula uses the concept of determinant geometry and gives the absolute area regardless of vertex order.
- Given area helps in forming an equation to find unknown coordinate values.
Calculation:
Given, vertices A(−3, 0), B(3, 0), C(0, k) and area = 9 sq. units
Using the formula: Area = (1/2) × |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
⇒ (1/2) × |−3(0 − k) + 3(k − 0) + 0(0 − 0)| = 9
⇒ (1/2) × |−3(−k) + 3k| = 9
⇒ (1/2) × |3k + 3k| = 9
⇒ (1/2) × |6k| = 9
⇒ |6k| = 18
⇒ 6k = ±18
⇒ k = ±3
∴ The value of k is 3 or −3.
Here Option 3 will be the correct answer.