>> Elementary Mathematics >> Area and perimeter

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Contents:

- Elementary Mathematics
- Area and perimeter
- Circles
- Clocks
- Factorisation
- Geometry
- Height and Distance
- Indices and Surd
- LCM and HCF
- Loci and concurrency
- Logarithms
- Polynomials
- Quadratic Equations
- Quadrilateral and parallelogram
- Rational expression
- Real Analysis
- Rectangular and Cartesian products
- Set theory
- Simple and Decimal fraction
- Simplification
- Statistics
- Straight lines
- Triangle
- Trigonometric ratio
- Trigonometry
- Volume and surface area

1). Find the area of a triangle whose sides measure 8 cm, 10 cm and 12 cm.
Given that, | ||||

2). The area of a right angled triangle is 40 sq cm. If its base is equal to 28 cm. find its height
Given that, area = 40 sq cm. base = 28 cm and height = perpendicular = ? Area = \( \Large \frac{1}{2}\times Base\times Perpendicular \) => 40 = \( \Large \frac{1}{2}\times 28\times Perpendicular \) Perpendicular =\( \Large \frac{40}{14}=\frac{20}{7} \) =\( \Large 2\frac{6}{7} \)cm | ||||

3). The three sides of a triangle are 15, 25 and x units. Which one of the following is correct?
In a triangle, Sum of two sides is always greater than 3rd side i.e., x < 25 + 15=40 ...(i) Difference of two sides is always less than 3rd side i.e., 25 - 15 =10 < x ...(ii) Form Eqs. (i) and (ii), we get 10 < x < 40 | ||||

4). A triangle with three equal sides has its area equal to \( \Large \Large 3\sqrt{3} \)sq cm. Find its perimeter.
According to the question, | ||||

5). The sides of a triangle area in the ratio of \( \Large \frac{1}{3}:\frac{1}{4}:\frac{1}{5} \) and its perimeter is 94 Cm.Find the length of the smallest side of the triangle.
Given ratio = \( \Large \frac{1}{3}:\frac{1}{4}:\frac{1}{5} \) | ||||

6). The area of an equilateral triangle is \( \Large \Large 4\sqrt{3} \)sq cm. Find the length of each side of the triangle
Area of equilateral triangle = \( \Large \frac{\sqrt{3}}{4}a^{2} \) => \( \Large 4\sqrt{3}=\frac{\sqrt{3}}{4}a^{2}\) => \( \Large a^{2} \)=16 a=\( \Large \sqrt{16} \)=4cm | ||||

7). The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle?
Since, the triangle is right angled. | ||||

8). If the area of an equilateral triangle is x and its perimeter is y. then which one of the following is correct?
Area of equilateral triangle \( \Large \frac{\sqrt{3} a^{2}}{4} \)=x ....(i) and perimeter = 3a = y => a = \( \Large \frac{y}{3} \) ...(ii) Now, putting the value of a from Eq. (ii) in Eq. (i), we get \( \Large \frac{\sqrt{3}\left(\frac{y}{3}\right)^{2}}{4} \)=x => x=\( \Large \frac{\sqrt{3}\times y^{2}}{9\times 4} \) => x=\( \Large \frac{y^{2}}{3\sqrt{3}\times 4} \) => x=\( \Large \frac{y^{2}}{12\sqrt{3}} \) => \( \Large 12\sqrt{3}x=y^{2} \) On squaring both sides, we get \( \Large y^{4}=432x^{2} \) | ||||

9). The area of an isosceles \( \Large \triangle ABC \) with AB = AC and altitude AD = 3 cm is 12 sq cm. What is its perimeter?
Let AB = CA = a cm and base = b cm
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10). The area of an equilateral triangle is \( \Large \Large \frac{\sqrt{243}}{4} \)sq cm. Find the length of its side.
According to the question, \( \Large \frac{\sqrt{3}}{4}a^{2}=\frac{\sqrt{243}}{4} \) => \( \Large a^{2}=\frac{\sqrt{81\times 3}}{\sqrt{3}}=\frac{9\sqrt{3}}{\sqrt{3}} \) a=\( \Large \sqrt{9} \)=3cm |