Mensuration Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Question : 16

Consider an equilateral triangle of a side of unit length. A new equilateral triangle is formed by joining the midpoints of one, then a third equilateral triangle is formed by joining the mid-points of second. The process is continued. The perimeter of all triangles, thus formed is

a) 6 units

b) 2 units

c) 3 units

d) Infinity

Question : 17

Two straight lines AB and AC include an angle. A circle is drawn in this angle which touches both these lines. One more circle is drawn which touches both these lines as well as the previous circle. If the area of the bigger circle is 9 times the area of the smaller circle, then what must be the angle A?

a) 75°

b) 45°

c) 60°

d) 90°

Question : 18

In the figure given above, LM is parallel to QR. If LM divides the ΔPQR such that area of trapezium LMRQ is two times the area of ΔPLM, then what is ${PL}/{PO}$ equal to?

a) $1/2$

b) $1/√2$

c) $1/√3$

d) $1/3$

Question : 19

The dimensions of a field are 15 m by 12 m. A pit 8 m long, 2.5 m wide and 2 m deep is dug in one corner of the field and the earth removed is evenly spread over the remaining area of the field. The level of the field is raised by

a) 25 cm

b) 15 cm

c) 20 cm

d) ${200}/9$ cm

Question : 20

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right-angle.
What is the area of quadrilateral ABCD ?

a) 312 $cm^2$

b) 300 $cm^2$

c) 306 $cm^2$

d) 316 $cm^2$