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 =$\frac{\sqrt{3}}{4}{a}^2$

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

=43.30$cm^{2}$

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$\pi$$cm^{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\pi$$cm^{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

= $90^{\cdot }$