Chapter 16: Mensuration

In measuring a quantity, the ratio of the quantity measured to the unit gives —

If a bench is $5$ metre long, then the number $5$ denotes —

Which of the following is NOT a quantity that mensuration measures directly?

The magnitude of a measured quantity equals —

Area of a triangular region with base $b$ and height $h$ is —

In any triangle $ABC$ with altitude $AD$ from $A$ to $BC$, the area is —

In a right-angled triangle with legs $a$ and $b$ adjacent to the right angle, the area equals —

The legs adjacent to the right angle of a right-angled triangle are $6$ cm and $8$ cm. Its area is —

The two legs of a right-angled triangle are $5$ cm and $12$ cm. Its area is —

If the legs of a right triangle adjacent to the right angle are $9$ cm and $12$ cm, what is the length of the hypotenuse?

If two sides of a triangle are $a$ and $b$ and the included angle is $C$, the area equals —

Two sides of a triangle are $9$ cm and $10$ cm with included angle $60°$. Its area is —

The approximate area of a triangle with sides $9$ cm and $10$ cm and included angle $60°$ is —

Two sides of a triangle are $4$ cm and $6$ cm with included angle $30°$. The area is —

Two sides of a triangle are $26$ m and $28$ m and the area is $182$ sq m. The included angle is —

For a triangle with sides $a, b, c$ and semi-perimeter $s = \dfrac{a+b+c}{2}$, the area is —

Sides of a triangle are $7, 8, 9$ cm. Its semi-perimeter is —

The approximate area of a triangle with sides $7, 8, 9$ cm is —

The perimeter of a triangle with sides $25, 27, 32$ cm is —

The area of a triangle with sides $25, 27, 32$ cm (semi-perimeter $42$) equals —

The area of an equilateral triangular region of side $a$ is —

The altitude of an equilateral triangle of side $a$ is —

The area of an equilateral triangle of side $4$ cm is —

The area of an equilateral triangle of side $6$ cm is —

If side of an equilateral triangle is $a$ and area increases by $3\sqrt{3}$ sq m when each side increases by $1$ m, then $a$ equals —

When each side of an equilateral triangle increases by $2$ m the area increases by $6\sqrt{3}$ sq m. The original side is —

If the perpendiculars from an interior point to the three sides of an equilateral triangle are $p_1, p_2, p_3$, the side $a$ satisfies —

If the three perpendiculars from an interior point of an equilateral triangle to the sides are $6, 7, 8$ cm, the length of a side is —

For an isosceles triangle with equal sides $a$ and base $b$, the height from the apex to the base is —

The area of an isosceles triangle with equal sides $a$ and base $b$ is —

An isosceles triangle has base $60$ cm and area $1200$ sq cm. The length of each equal side is —

The equal sides of an isosceles triangle are $10$ m and the area is $48$ sq m. The base is —

An isosceles triangle has perimeter $16$ m, with each equal side $\dfrac{5}{6}$ of the base. The base is —

With perimeter $16$ m and each equal side $\dfrac{5}{6}$ of the base, each equal side measures —

Two roads make an angle $120°$ at a place. Two persons walk for $5$ hours at $10$ km/h and $8$ km/h respectively. The direct distance between them squared (in km²) is —

Approximate direct distance between the two persons in the previous problem is —

In right-angled triangle $ABC$ with right angle at $B$, $AB = 15$, $AC = 25$. Then $BC$ equals —

With $AB=15$, $BC=20$, $AC=25$ and $BD\perp AC$, the length $BD$ equals —

In the same triangle, $AD$ equals —

The ratio of areas $\triangle ABD : \triangle BCD$ in the above figure is —

The hypotenuse of a right triangle is $25$ m and one side is $\dfrac{3}{4}$ of the other. The two sides are —

A $20$ m ladder stands vertically against a wall. If the upper end descends $4$ m, the lower end moves further by —

Two sides of a triangle are $25$ cm and $27$ cm; perimeter is $84$ cm. The third side is —

The semi-perimeter of a triangle with sides $25, 27, 32$ cm is —

Equal sides of an isosceles triangle are $10$ m, area $48$ sq m. Two possible values of the base (m) are —

Two persons walk along roads making $135°$ at $7$ km/h and $5$ km/h for $4$ hours. The square of the direct distance (km²) is approximately —

Length of rectangle is $a$, breadth $b$. Its area is —

Perimeter of a rectangle of length $a$ and breadth $b$ is —

Diagonal of a rectangle of length $a$ and breadth $b$ is —

Length of a rectangular room is $\dfrac{3}{2}$ of its breadth. Area is $384$ sq m. Breadth is —

With area $384$ sq m and length $\dfrac{3}{2}\times$ breadth, length equals —

The perimeter of the rectangle in the above problem is —

Approximate length of diagonal of a rectangle of $24$ m by $16$ m is —

Area of a rectangle is $2000$ sq m. If length is reduced by $10$ m it becomes a square. The length and breadth are —

Area of a rectangle is $160$ sq m. If length is reduced by $6$ m it becomes a square. The breadth is —

Length of a rectangle is twice its width and area is $512$ sq m. Its perimeter is —

If the length of a side of a square is $a$, its area is —

Perimeter of a square of side $a$ is —

Diagonal of a square of side $a$ equals —

The area of a square road around a $4$-m-wide road inside it equals $1$ hectare. The side of the field (outer) is —

$1$ hectare equals —

Number of $40$-cm square stones needed to pave a square of side $24$ m is —

Area of a parallelogram with base $b$ and height $h$ is —

Area of a parallelogram in terms of a diagonal $d$ and the perpendicular $h$ from the opposite vertex on that diagonal is —

The area of a parallelogram is $120$ sq cm and a diagonal is $24$ cm. The perpendicular from the opposite vertex on the diagonal is —

The base of a parallelogram is $\dfrac{3}{4}$ of the height; area is $363$ sq inches. The height is —

With the height $22$ in and base $\dfrac{3}{4}\cdot 22$ in, the base equals —

A parallelogram has base $125$ m and height $5$ m, with area equal to a square's area. The square's diagonal is —

Sides of a parallelogram are $12$ m and $8$ m and the smaller diagonal is $10$ m. The semi-perimeter of one of the triangles formed by the diagonal is —

In the above parallelogram the other diagonal is approximately —

The area of a rhombus with diagonals $d_1$ and $d_2$ is —

The diagonals of a rhombus —

A diagonal of a rhombus is $10$ m and area is $120$ sq m. The other diagonal is —

With diagonals $10$ m and $24$ m, each side of the rhombus is —

The perimeter of a rhombus with side $13$ m is —

Perimeter of a rhombus is $180$ cm and the smaller diagonal is $54$ cm. Each side is —

With perimeter $180$ cm and one diagonal $54$ cm, the other diagonal is —

Area of the above rhombus (diagonals $54$ and $72$ cm) is —

The area of a trapezium with parallel sides $a$ and $b$ and perpendicular distance $h$ between them is —

Two parallel sides of a trapezium are $91$ cm and $51$ cm; the other two sides are $37$ cm and $13$ cm. The perpendicular distance between the parallel sides is —

The area of the trapezium with parallel sides $91, 51$ cm and other sides $37, 13$ cm is —

Difference between the parallel sides of a trapezium is $8$ cm and their perpendicular distance is $24$ cm. If area is $312$ sq cm, the longer parallel side is —

In the above trapezium the shorter parallel side is —

Area of a trapezium with parallel sides $10$ cm and $6$ cm and height $4$ cm is —

A square field has a $4$-m-wide road inside its border. If the road's area is $1$ hectare, the inner side of the field (without road) is —

Plot of $80$ m by $60$ m has a pond inside, with $4$-m-wide border. The pond dimensions are —

With plot $80\times 60$ and border width $4$ m around the pond, the area of the border is —

A square has a $5$-m-wide path outside it; path area is $500$ sq m. The side of the square is —

The perimeter of a square equals that of a rectangle whose length is thrice its breadth and area $768$ sq m. The breadth of the rectangle is —

With the rectangle of area $768$ sq m and length $:$ breadth $= 3 : 1$, the side of the square having same perimeter is —

Sides of a parallelogram are $30$ cm and $26$ cm and the smaller diagonal is $28$ cm. The semi-perimeter of the triangle formed by the diagonal is —

Area of a regular polygon with $n$ sides each of length $a$ equals —

Each interior angle of a regular polygon with $n$ sides is —

The half-angle at a vertex of the isosceles triangle formed by joining the centre of a regular $n$-gon to two adjacent vertices is —

The area of a regular pentagon of side $4$ cm (use $\cot 36° \approx 1.376$) is approximately —

For a regular hexagon, each central angle subtended by a side at the centre is —

The triangle formed by joining the centre of a regular hexagon to two adjacent vertices is —

If the distance from centre to vertex of a regular hexagon is $4$ m, the area of the hexagon is —

If each side of a regular hexagon is $5$ cm, its area equals —