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Class 9 Maths HOTS Questions - Areas of Parallelograms
Question 1. If two sides of one triangle are equal to the two sides of another triangle and the contained angles are supplementary; show that the two triangles are equal in area.
Let ∆ABC and ∆DEF are such that AC = DE; CB = EF and ∠ABC + ∠DEF = 180°.
Now, allow ∆DEF fall along ∆ABC such that DE falls on AC and B and F are on opposite directions.
∵∠ACB + ∆DEF = 180°
⇒ BCF is a straight line
∴ We get a ∆AFB, in which C is mid point of FB.
∴ AC is median of ∆AFB, Median divides the ∆ into two triangles equal in area.
⇒ ar (∆AFC) = ar (∆ABC)
⇒ ar (∆DEF) = ar (∆ABC).
Question 2. In a trapezium ABCD, where AB || DC, E is the mid point of BC. Prove that ∆AED = ½ trap. ABCD.
Hint: Through E, draw FEG || AD meeting AB and CD in F and G respectively.
∴∆ BEF ≅ ∆ CEG
⇒ ar trap. ABCD = ar (||gm ADGF)
⇒ ∆ AED = ½ ||gm ADGF
FAQs on Class 9 Maths HOTS Questions - Areas of Parallelograms
| 1. What is the formula to find the area of a parallelogram? |  |
| 2. How do you find the height of a parallelogram if only the base and area are given? | |
Ans. If the base and area of a parallelogram are given, the height can be found by dividing the area by the base. Thus, the height (h) can be calculated using the formula h = A / base, where A represents the area and base is the length of the base.
| 3. What is the difference between the area of a parallelogram and the area of a triangle? | |
Ans. The main difference between the area of a parallelogram and the area of a triangle is that the area of a parallelogram is calculated by multiplying the base by the height, whereas the area of a triangle is calculated by multiplying half of the base by the height.
| 4. How do you find the area of a triangle when the base and height are given? | |
Ans. To find the area of a triangle, when the base and height are given, you can use the formula A = (1/2) × base × height. Here, A represents the area, base is the length of the base, and height is the corresponding height of the triangle.
| 5. Can the area of a parallelogram be negative? | |
Ans. No, the area of a parallelogram cannot be negative. The area represents the measure of the region enclosed by the parallelogram, and it is always a positive value. If any negative value is obtained during calculations, it indicates an error in the calculations.
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