A trapezium ABCD where AB || CD. Ratio of AB : CD = 5 : 9. If the area of triangle COD is 81 units, then find the area of triangle AOB. (O is the meeting point of diagonals)

Find the length of the median of the triangle with sides 10 cm, 11 cm, and 12 cm respectively. (Median bisects the side of 12 cm)

The areas of two squares are 16:9. The ratio of their perimeter is :

If the base of an equilateral triangle is 8 cm, then find its area.

In an isosceles triangle, if the unequal side is 8 cm and equal side is 5 cm. then the area of the triangle is:

The sides of a triangle are in the ratio 3 : 4 : 5, the triangle is:

PQRS is a trapezium in which PQ is parallel to RS and PQ = 4(RS). The diagonals of the trapezium intersect at O. What is the ratio of the area of triangle SRO to the area of the triangle PQO?

In ∆ABC, AD is the internal bisector of ∠A, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is:

The area of a triangle is 1470 cm². If the base of this triangle is (3/5)^th of the height corresponding to that base, then what will be the height of the triangle?

The areas of the two triangles are in the ratio 4 : 3 and their heights are in the ratio 6 : 5. Find the ratio of their bases.

In a triangle, ABC, AB = 6 units, BC = 8 units, and AC = 10 units. Let M be a point on AC such that BM = 5 units. With a point D, a triangle BMD is formed, and the triangle BMD is similar to the triangle ABC with \(\frac{BM}{AB}=\frac{BD}{AC}\). What is the length of BD in units?

What is the area of a triangle whose sides are 7 cm, 24 cm and 25 cm?

Find the area ( in cm²) of the traingle whose height is 48 cm and the base is \(\frac{1}{6}\) the length of the height?

When the side of an equilateral triangle is made three times the original side, the area of the new equilateral will become:

What is the area of a right-angled triangle, the length of whose sides are 10 cm, 24 cm and 26 cm?

The parallel sides of an isosceles trapezium are 20 cm and 34 cm. If the one of the non-parallel sides has length 25 cm, what is the area (in cm²) of the trapezium?

It is given that Triangle ABC ~ Triangle YZX and Ar ABC : Ar XYZ = 256 : 25. If AB = 12 cm, BC = 10 cm, CA = 15 cm, then what is the value of YZ (in cm)?

The distance between the opposite sides of a parallelogram is 10 cm. One side of the parallelogram is 30 cm. Find the area of the parallelogram.

The side of an equilateral triangle is equal to the diagonal of a rectangle whose sides are 9 cm and 12 cm. Find the area (in cm²) of the equilateral triangle.

If the sides of a triangle MNO are 15 cm, 112 cm, and 113 cm then, find the area of the triangle. (in cm²)

If the inradius of a triangle with a perimeter 32 cm is 6 cm, then the area of the triangle in cm² is -

Which of the following sets cannot be the values of lengths of sides of a triangle?

There are two similar triangles, ABC and PQR. The ratio of the area of these two triangles is 49 : 25. Find the ratio of (AX - PY) : (AX + PY) where X and Y is a perpendicular of side BC and QR respectively:

In the figure given below, PQRS is a trapezium and QO is perpendicular to RS. If QO = 6 cm, RS = 22 cm, and the area of the trapezium is 78 cm², then what is the length of side QR?

A trapezium ABCD where AB || CD and O is the meeting point of its diagonals. The ratio of AB : CD is 5 : 9. If the area of triangle COD is 81 units. Find the area of triangle AOB.

In triangle ABC, if AB = 16 cm, AC = 10 cm, and ∠BAC = 60^o, then find the length of the side BC.

Find the value of AP in the given figure, if BP and BC are 4 cm and 7 cm, respectively.

The area of triangle P is 55% of the area of triangle Q. If the sides of the triangle Q are 7 cm, 12 cm and 15 cm. What will be the area (in cm²) of the triangle P?

The area of a triangle is 1470 cm². If the base of this triangle is (3/5)th of the height corresponding to that base, then what will be the height of the triangle?

The sides other than hypotenuse of the right-angle triangular park are in ratio 3 : 4. The sum of all sides is 144 m. Find the area of the triangular park.

If the length of the three sides of the triangle is 36, 45, and 27cm then what is the area of the triangle?

If the length of the three sides of the triangle is 36, 45, and 27 cm then find the area of the triangle.

The perimeter of an equilateral triangle is 48 cm. Find its area (in cm²).

The sides of a triangle ABC are 40cm, 42cm, and 58cm. If the area of triangle ABC is equal to the area of the isosceles right angle triangle PQR, then find the measure of equal sides of the isosceles right angle triangle PQR.

One of the sides of a triangle is 7 cm and the perimeter of the triangle is 18 cm. If the area of the triangle is √108 cm² then, find the other 2 sides of the triangle. (in cm)

The sides of a triangle are in the ratio of \(\frac12 ∶ \frac13 ∶\frac1 4\) . If the perimeter is 52 cm, then the length of the smallest side is:

The area of a right angled triangle is 84 cm² and one of its perpendicular sides is 24 cm. If the perimeter of a square is equal to the perimeter of the triangle, what is the area (in cm²) of the square?

The lengths of sides of a triangle are in the ratio 3 : 4 : 5. If the perimeter of the triangle is 72 cm, find the length of the largest side.

The ratio between perimeter of an equilateral triangle and a square is 3 : 8. The area of square is 800% of area of a rectangle having sides 8 m and 4 m. Find the perimeter of triangle.

The area of a right angled triangle is 84 cm² and one of its perpendicular sides is 24 cm. If the perimeter of a square is equal to the perimeter of the triangle, what is the area (in cm²) of the square?

In an equilateral triangle, ABC having side a, three perpendiculars P₁, P₂, and P₃ are drawn to BC, AB, and AC from the center. Also, the sum of the lengths of perpendiculars is equal to 63 cm. Find the value of a. (in cm.)

ABCD a trapezium and the length of A and B is 20 m and the length of C and D is 15 cm. If the height of the trapezium is 10 m, then find the area of the trapezium.

The in-radius of a triangle is 8 cm, and the sum of the lengths of its sides is 125 cm. The area of the triangle (in cm²) is:

Three altitudes of length 1.5√3 m, 10√3 m, and 4.5√3 m are drawn on every side of an equilateral triangle from a point that lay inside the triangle. Find the perimeter of the equilateral triangle.

Find the height of the triangle whose area is equal to the area of a rectangle.

Statement I. The ratio between the length and breadth of the rectangle is 3 : 2.

Statement II. The base of the triangle is 16 cm.

Statement III. The perimeter of the rectangle is 80 cm.

In a right angle triangle ABC, ∠B = 90°. AM and CN are the two medians on sides BC and AB respectively, such that AM = 10 cm and CN = 5 cm. Find the value of AC.

In a triangle ABC, AB is 20% more than that of BC and AC is 50% more than that of AB. If the perimeter of the triangle is 120 cm, find the area (in cm²) of the triangle. (approx.)

In the given figure, the ratio of AE : CE = 5 : 3, EB = 30 cm and AB = 75 cm. What is the value of CD?

ABC is a triangle with sides of 6 cm, 4 cm, and 6 cm. D, E, and F are the midpoints of the sides AB, BC, and AC respectively. What is the area of the triangle DEF (in cm²)?

Point M and N are on the sides PQ and QR respectively of a triangle PQR, right angled at Q. If PN = 9 cm, MR = 7 cm and MN = 3 cm, then find the length of PR (in cm).