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

In a triangle ABC, AB = 8 cm and AC = 5 cm. What is true about the value of side BC?

In a right angled triangle, perpendicular sides are 45 cm and 60 cm. Find the length of the perpendicular drawn from the vertex to its hypotenuse.

ABCD is a square and points X and Y are on the lines AB and BC respectively such that, XY || AC. If BY : YC = 1 : 3 and area of triangle BXY is 450 cm², find AC.

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

△ABC and △QPR are similar triangles. Area of △ABC and △QPR are 1296 m² and 5184 m² respectively. If the side AB is 12 m, then find the length of PQ.

In the given fig. ABCD is a trapezium such that AB II CD. NC = 6 cm, AB = 10 cm and DM = NC. AM and BN are two perpendiculars on the side CD. DM = AM. Find the area of the trapezium ABCD.

Sides of a triangle are 12 cm, 9 cm and 9 cm. What is the radius of the circumcircle of this triangle?

The side of an equilateral triangle is 16 cm. Find the ratio of its area to its perimeter.

X, Y, and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm, respectively, then what is the length of Z?

The perimeters of two similar triangles ABC and PQR are 156 cm and 46.8 cm, respectively. If BC = 19.5 cm and QR = x cm, then the value of x is:

The length of the base of a triangle is 3 cm smaller than the length of its altitude. Its area is 104 cm². What is the length of the base?

If the area of a parallelogram is 508 m² and its base is 40 m, then what is the corresponding height of the parallelogram?

The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 90 cm. Find its area (in cm²).

If D is the midpoint of BC in △ABC and ∠A = 90⁰, then AD = _______.

In ∆ABC, AB = 7cm, BC = 10cm, and AC = 8cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then DC (in cm) =?

The two parallel sides of a trapezium are 27 cm and 13 cm, respectively . If the height of the trapezium is 7 cm, then what is its area in m² ?

What is the area (in m², up to 1 place of decimal) of an equilateral triangular field of side 8.5 m?

In  ∆MNO, ∠N = ∠O and NO = 12 cm, MO = 10 cm and MP be the altitude, then the length of MP is:

ΔABC is similar to ΔPQR, and PQ = 10 cm. If the area of ΔABC is 32 cm² and the area of ΔPQR is 50 cm², then the length of AB (in cm) is equal to:

ΔABC is an equilateral triangle with a side of 12 cm. CD is the bisector of ∠C which meets AB at D, and E is the mid-point of CD. What is the length of BE?

In ΔPQR, the length of the side QR is less than twice the length of the side PQ by 3 cm. Length of the side PR exceeds the length of the side PQ by 14 cm. The perimeter is 55 cm. The length of the smaller side of the triangle PQR is:

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?

In △ABC, D and E are the points on sides AB and AC, respectively, such that DE ll BC. If AD = x, DB = x - 2, AE = x + 2, and EC = x - 1, then (AB + EC) is equal to (all measurements in cm):

In a triangle DEF, DP is the bisector of ∠D, meeting EF at P. If DE = 14 cm, DF = 21 cm, and EF = 9 cm, find EP.

Find x if ABCD is a parallelogram as given in figure below, with two diagonals AC and BD intersecting at O and OA = x + 3, OB = y + 2, OC = 2x + y, OD = 3y

In a parallelogram, one of the parallel sides is 16 cm and the other side is 12 cm. If the perpendicular distance between the two parallel sides of dimension 16 cm is 24 cm, then the perpendicular distance between its other two parallel sides is :

In △STU, X and Y are the points on sides ST and SU, respectively. XY is parallel to TU. If SX: XT = 2 : 5 and UY = 20 cm, then what is the value of SU?

In \(\triangle\)ABE, D and C are the points on sides AE and EB, respectively, such that DC II AB. If AD = 4 cm, BC = 5 cm, DC = 10 cm, and AB = 15 cm, then the sum of the lengths of DE and EC is:

In the given figure, ABCD is a rectangle and P is a point on DC such that BC = 24 cm, DP = 10 cm, and CD = 15 cm. If AP produced intersects BC produced at Q, then find the length of AQ. 

ΔABC ~ ΔPQR, AB = 12 cm, PQ = 18 cm, and the perimeter of ΔABC is 45 cm. Find the perimeter of ΔPQR.

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.

ΔABC is an equilateral triangle with a side of 12 cm. CD is the bisector of ∠C which meets AB at D, and E is the mid-point of CD. What is the length of BE?

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

In an isosceles trapezium, the lengths of the parallel sides are 3 cm and 9 cm and the length of altitude is 4 cm. What is the ratio of the perimeter and the area of the trapezium?

Two similar triangles ABC and PQR have perimeters 15 cm and 25 cm respectively. If the area of ABC is 108 sq.cm, find the area of PQR.

The area of an equilateral triangle is 4\(\sqrt{3}\) cm². Find the side (in cm) of the triangle.

The area of ΔABC is 104 cm². If D is the midpoint of BC and E is the midpoint of AB, then the area (in cm²) of ΔBDE is :

In the figure given below, the lengths of sides AB, BC, and AC of the triangle ABC are 4 cm, 8 cm, and 6 cm respectively. If AD is the median of the triangle and G is the centroid, then what is the length of DG (in cm)?

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

In a triangle XYZ, M, and N are the points on sides XY and XZ respectively such that MN || YZ. MN = 3 cm and YZ = 6 cm. Find the ratio of the area of triangle XYZ and parallelogram MNZY.

The ratio of one of the corresponding sides of the two similar triangles is 4 : 5. If the area of the first triangle is 96 cm². Find the area of the second triangle.

In the given figure, if AB = 8 cm, AC = 10 cm, ∠ABD = 90^o and AD = 17 cm, then the measure of (CD + AC) is:

A scalene triangle ABC is given with sides 15 cm, 13 cm, and 12 cm, and a circle is drawn in the triangle having radius r. Find the value of r.

In a triangle ABC, AB = 12, BC = 18 and AC = 15. The medians AX and BY intersect sides BC and AC at X and Y respectively. If AX and BX intersect each other at O, then what is the value of √2 × OX?

In the given figure AL ⊥ BD, CM ⊥ BD. BD = 15 cm, AL = 4 cm, and CM = 6 cm. Find the value of (Area of △BCD - Area of △ABD).

D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and AD : DB = 5 : 4, CD and BE intersect each other at F. Then the ratio of the areas of ΔDEF and ΔCBF:

If the perimeter of a regular hexagon is 684 cm, then find the area of the hexagon.

A scalene triangle ABC is given with sides 15 cm, 13 cm, and 12 cm, and a circle is drawn in the triangle having radius r. Find the value of r.