Geometry and Mensuration: Test 29

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These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.
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Geometry and Mensuration: Test 29

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Question 1

The area of a ΔABC is equal to area of square of side length 6 cm. What is the length of the altitude to AB where AB = 9 cm?

A	18 cm
B	14 cm
C	12 cm
D	8 cm

Question 1 Explanation:

$ \begin{array}{l}\frac{1}{2}altitude\times 9=36\\=>altitude=8\end{array}$

Question 2

What is the area of an equilateral triangle having altitude equal to 2√3 cm?

A	√3 sq cm
B	2√3 sq cm
C	3√3 sq cm
D	4√3 sq cm

Question 2 Explanation:

$ \begin{array}{l}Let\text{ }the\text{ }side\text{ }of\text{ }the\text{ }triangle\text{ }=\text{ }x\text{ c}m\\\frac{\sqrt{3}}{4}{{x}^{2}}=\frac{1}{2}\times 2\sqrt{3}x\\=>x=4.\\Area=4\sqrt{3}sq.cm.\end{array}$

Question 3

A lawn 30m long and 16m wide is surrounded by a path 2 m wide. What is the area of the path?

A	200 m²
B	280 m²
C	300 m²
D	320 m²

Question 3 Explanation:

Area of the path= (30+2x2)(16+2x2)-30x16=200m². Correct option is (a)

Question 4

A circle circumscribes a rectangle with side 16 cm and 12 cm. What is the area of the circle?

A	48 π sq cm
B	50 π sq cm
C	100π sq cm
D	200π sq cm

Question 4 Explanation:

$\begin{array}{l}The\text{ }diameter\text{ }=\sqrt{{{16}^{2}}+{{12}^{2}}}=\sqrt{400}=20cm\\The\text{ }area\text{ }of\text{ }circle\text{ }=\text{ }100\pi ~sq\text{ }cm.\\Correct\text{ }option\text{ }is\text{ }\left( c \right)\\\end{array}$

Question 5

The lengths of two sides of a right angled triangle which contain the right angle are ‘a’ and ‘b’ respectively. Three squares are drawn on the three sides of the triangle on the outer side. What is the total area of the triangle and the three squares?