Geometry Formulas

Question 1: Ratan had a hard wooden board out of which he made an equilateral triangle with a side length of 10 cm. Find it’s area?

Answer: The formula to find the area of an equilateral triangle is given by A =\frac{\sqrt{3}}{4}{a}^2

=\frac{\sqrt{3}}{4}{10}^2

=43.30cm^{2}

Question 2: Raj bought a mirror for his room  with a length of 12 meters and a diagonal of 15 meters, find the width of the rectangle.

Answer:  The width of the rectangle is 9 meters.

 In a rectangle, the diagonal divides the rectangle into two congruent right-angled triangles. We can use the Pythagorean Theorem to find the width (‘b’) of the rectangle using the length (‘a’) and the diagonal (‘c’):

b^{2} =c^{2} – a^{2}
b^{2} = 15^{2} – 12^{2}
b^{2}=225-144
b^{2}= 81
b=\sqrt{81}
b = 9 m

Question 3: Sam made a circle out of clay find it’s area in terms of pi given the diameter of circle is 18cm?

Answer: Given Diameter = 18 cm

Radius = 9 cm

Area of circle = \pi r^{2}

Area = \pi 9^{2}

Area= 81\picm^{2}

Question 4: Find Volume of a ice-cream cone whose radius is 6 cm and height 7 cm?

Answer: We know Volume of cone  = \frac{1}{3}\pi r^{2}h

Hence, \frac{1}{3}\pi r^{2}h = \frac{1}{3}\pi 6^{2}7

=84\picm^{3}

Question 5: The supplement of 90^{\cdot } is?

Answer: Supplementary angles means those angles whose sum is 180.

According to question:

90^{\cdot } + x = 180

= 180- 90 = x

= 90^{\cdot }