The height of an equilateral triangle is 10 cm. find its area.

Answer: Option D

Explanation:

As far as questions of Area or Volume and Surface area are concerned, it is all about formulas and very little logic. So its a sincere advice to get all formulas remembered before solving these questions.

Lets solve this,

$$\begin{aligned} \text{Area of rectangle =}l*b\\ \text{Area of triangle =}\frac{1}{2}l*b\\ \text{Ratio =}l*b:\frac{1}{2}l*b \\ = 1:\frac{1}{2} \\ = 2:1 \end{aligned}$$

One little thing which should be taken care in this type of question is, be sure you are calculating ration in the given order of the question.
If it is ratio of triangle and rectangle then we have to write triangle formula first. cheers :)

Answer: Option A

Explanation:

$$\begin{aligned} \text{We know }h^2 = b^2+h^2 \\ =>\text{Other side }= \sqrt{(17)^2-(15)^2} \\ = \sqrt{289-225} = \sqrt{64} \\ = 8 meter \\ Area = Length \times Breadth \\ = 15\times8 m^2 = 120 m^2 \end{aligned}$$

Answer: Option C

Explanation:

Let each side be a cm, then
$$\begin{aligned} \left(\frac{a}{2}\right)^2+{10}^2 = a^2 \\ <=>\left(a^2-\frac{a^2}{4}\right) = 100 \\ <=> \frac{3a^2}{4} = 100 \\ a^2 = \frac{400}{3} \\ Area = \frac{\sqrt{3}}{4}*a^2 \\ = \left(\frac{\sqrt{3}}{4}*\frac{400}{3}\right)cm^2 \\ = \frac{100}{\sqrt{3}}cm^2 \end{aligned}$$

Answer: Option C

Explanation:

Let the original radius be R cm. New radius = 2R

$$\begin{aligned} Area = \pi R^2 \\ \text{New Area =} \pi {2R}^2 \\ = 4\pi R^2 \\ \text{Increase in area =}(4\pi R^2 - \pi R^2) \\ = 3\pi R^2 \\ \text{Increase percent =} \frac{3\pi R^2}{\pi R^2}*100 \\ = 300 \% \end{aligned}$$

Answer: Option D

Explanation:

Area of each slab =
$$\begin{aligned} \frac{72}{50}m^2 = 1.44 m^2\\ \text{Length of each slab =}\sqrt{1.44} \\ = 1.2m = 120 cm \end{aligned}$$