Heron`s Formula...

In the given figure, if the perimeter of the trapezoid is 34 cm, what will be the area of triangle ADB?

In a triangle, the lengths of two of the sides are 10 cm and 14 cm. If the perimeter of the triangle is 30 cm, what will be its area?

In the given figure, area of the isosceles triangle = cm², length (BD) of the triangle = 8 cm. Find the measures of the other sides of the isosceles triangle.

In a scalene triangle, the three sides are a, b and c. The ratio of a to b is 2 : 3 and that of b to c is 2 : 3. If the semiperimeter of the triangle is 19 cm, find the area of the triangle (round to the nearest whole number).

A rhombus shaped park has a perimeter of 80 m and 24 m long diagonal. If grass is laid on the park and the total amount spent on it is Rs. 28,800, what is the per m²cost of laying the grass?

What will be cost of painting a triangle at the rate of 25 paise per cm² if the sides of the triangle are (x - 1), (x + 1) and (x – 3), and the perimeter is 84 cm?

A parallelogram having a base of 25 m is made up of two triangles such that the dimensions of each small triangle are 17 m, 12 m and 25 m. What will be the height of the parallelogram?

Two of the sides of a triangle are 12 cm and 16 cm. What will be the value of r if the perimeter of the triangle is 50 cm, and the area of the triangle is cm²?

The perimeter of a triangular wall shelf is 126 cm. What will be the area of the shelf if the largest side of the shelf is 3 times the smallest side of the shelf, and the remaining side is 50 cm long?

Triangle ABC has a perimeter of 34 cm. If (s - a) = 7 cm and (s - b) = 6 cm, what will be the area of the triangle, given that a and b are two sides of the triangle, and s is the semiperimeter?

There are two isosceles triangles. The two equal sides of the bigger isosceles triangle are equal to (x + 2) units and the remaining side of the bigger isosceles triangle is four more than double the unequal side of the smaller isosceles triangle. In the smaller isosceles triangle, an angle bisector, which measures 12 units, is drawn from its vertex to the side which measures different from other sides. The unequal side of the smaller isosceles triangle is of 10 units, and the two equal sides of the smaller triangle are of x units length. What is the difference between the areas of both the triangles?

In the given figure, DCF is an isosceles triangle with two of its sides equalling 12.5 cm each. What would be the ratio of the area of rhombus ABCD to the area of the shaded region if the diagonals of rhombus ABCD are 32 cm and 24 cm long?

In a right-angled parallelogram, the smaller side is 5 units and a diagonal is 13 units long. The angle of the parallelogram is changed now but the measure of each side is identical. A point on the larger side of the parallelogram is such that it divides the larger side of the parallelogram in two equal parts. From that point, a line which measures 5 units is drawn to any of the opposite vertices.

What would be the difference between the area of the right-angled triangle and that of the new isosceles triangle?

Find the area of the shaded region if △GEF is an isosceles triangle, where GE = GF, the lengths of its sides are 13 cm, 13 cm and 10 cm, and the sum of the parallel sides of the trapezium ABCD is 38 cm.

The sides of a triangle, formed by a piece of wire, are 30 cm, 30 cm and 28 cm. If the same wire is molded to form a circle, then what is the increase in the area covered by these two shapes? (Take π =and )

The following shape has been cut out from a square shaped piece of origami paper having sides equal to 20 cm each. Find the total area of the left over paper after removal of this shape, provided that the four small triangles are identical and the shape is square.

In a cemented circular playground of a play-way, % of the area is covered by 6 triangles of the same size, which are made for the children for extra-curricular activities. If the sides of each triangle are 3 m, 4 m and 5 m, then find the perimeter of the circular ground. (pi = 22/7)

State 'T' for true and 'F' for false for each of following.

1. Altitude to the smallest side of the triangle, having sides 28 cm, 15 cm and 41 cm, is 16.8 cm.
2. If the sides of a triangle are in ratio 7 : 8 : 9, the area will be more than 250 cm², provided that the perimeter is 72 cm.
3. Two triangles are made by drawing a diagonal in a parallelogram. If the semiperimeter of a triangle is given, we can find the area of the parallelogram, provided that the lengths of a diagonal and a base of the parallelogram are given.
4. Mr. Sharma decided to take a triangular piece of land on rent for a period of 6 months. If the sides of the triangle are 40 m, 24 m and 32 m, he will pay Rs. 25,000, provided that the yearly rent is Rs. 125 per m².

A field is in the shape of a trapezium. The owner of this field occupies this field at a rate of Rs. 650 per sq m per year. The parallel sides of this field are 49 m and 24 m and the non-parallel sides are 12 m and 17 m. A farmer occupies this field for 5 months. How much will he pay after 5 months?

Pahul is preparing a crown from a cardboard. She has joined three triangles and a rectangle to form this crown. Two identical triangles, which are joined at the ends, have three sides which measure 61 cm, 60 cm and 11 cm. The triangle which is at the middle has three sides which measure 50 cm, 24 cm and 34 cm. The base of this crown is in the shape of a rectangle whose length is 46 cm and width is 13 cm. What will be the area of this crown?

Sameer makes a bird by cutting coloured paper in triangles of different sizes. Each of the length is in cm. If the cost of the coloured paper is Rs. 14 per m², what is the the approximate cost of making this whole bird? ()

Samya joined some identical triangular and square pieces of cardboard together to make multiple little wall hangings. One of them is given in the figure below (Not to the scale). Find the total area of the wall hanging.

Harmeet wants to put a boy scout symbol outside his place which is made up of 4 similar isosceles triangles as shown below. The area shared by the four triangles is 60% of the the total area of the four triangles. The area shared by the four triangles is to be coloured silver and the rest is to be coloured golden. If the cost of silver paint is 30 paise/cm² and that of golden paint is 70 paise/cm², then find the total cost to be incurred in painting the symbol, given that the base of the triangle is 24 cm and the other two sides are 15 cm each.

Somya made a paper boat by joining 3 triangles as shown. What is the total area of the boat?