Heron`s Formula...

The ratio of the unequal side to the perimeter of an isosceles triangle is 1 : 5. Find the area of the triangle if its semi-perimeter is 7.5 cm.

In a circle with centre O and chord AB = 8 cm, the area of the shaded part is 66 cm². Find the area of triangle AOB. (Use = 22/7)

In the given triangle, AB + AC = 8 cm and AB + BC = 10 cm. Find the area of the triangle.

The circumference of the given circle with centre O is 44 cm. What will be the approximate area of triangle AOB if M and N are the mid-points of OA and OB, respectively? (Use = 22/7)

The perimeter of a triangle whose sides measure (3x + 4) cm, (2x + 1) cm and (4x - 5) cm is 36 cm. Find the area of the triangle.

The area of an isosceles triangle, whose base is 8 cm, is 12 cm². What is the length of each equal side?

What is the area of an isosceles triangle in which the product of an equal side and the unequal side is 35 and the sum of equal sides is greater than 10 but less than 15?

The area of a triangle with sides of lengths 2 cm, 2p cm and p cm is . What is the value of p?

In a regular pentagon PQRST, a triangle is made by drawing diagonals from a vertex. If the perimeter of triangle PTS is 56 cm, what will be the area of the triangle PSR provided that the perimeter of the pentagon is 90 cm?

The sides of a triangle measure x + 2, x + 4 and 2x + 2. If the perimeter is 48 cm, then what will be the area of the triangle?

A triangular plot is rented for a period of 4 months. The sides of the plot are 20 m, 24 m and 28 m. How much rent will one pay, if the yearly rent is Rs. 4200 per m²?

A triangle has area 9000 cm² and semi-perimeter 270 cm. What will be the difference between the lengths of the two missing sides, if one side measures 120 cm?

Find the area of an isosceles triangle with base 6 cm and the length of each equal side as 5 cm.

A man was making a quadrilateral shape; he took a piece of orange paper with sides 6 cm, 5 cm and 9 cm. He pasted another white paper with sides 6 cm, 8 cm and 10 cm adjacent to the previous paper. He drew a line dividing the paper into two parts from the mid-point of the longest side to the opposite vertex and coloured the central part as blue and rest of the quadrilateral shape white. How much area of the quadrilateral shape is coloured orange, blue and white?

In the following diagram, BC is the diameter of the circle. AB = 10 cm, AC = 24 cm, BD = 13 cm and CD = 15 cm. What is the area of quadrilateral ABCD?(Take = 3.7)

The perimeter of the following shape is 40 cm and that of the square in between the shape is 24 cm. If all of the triangles are congruent to each other and of same size, find the area of the shape given that all the triangles are isosceles.

In the given parallelogram ABCD, AB = 12 cm and AC is the diagonal. If the semi-perimeter of △ADE is 12 cm and AE = 10 cm, then what is the difference between the areas of △AEC and △ABC, given that E is the mid-point of DC?

A farmer is trying to create a fence around his field, which is in the shape of a rhombus. He uses 320 m of the fencing wire. If the length of the diagonal of the field is 100 m, then what will be its area?

In a triangle ABC with sides 12 cm, 17 cm and 25 cm, find the difference between the altitudes which can be made from the shortest and longest sides of the triangle.

If the equal sides of an isosceles triangle ABC are '2m' units each and the third side is 'n' unit , then which of the following will represent the area of 4 such triangles?

Find the perpendicular height of a parallelogram ABED formed inside a trapezium ABCD with total area of 196 cm². The triangle formed inside the trapezium has a base of 15 cm, with sides BE and BC measuring 14 cm and 13 cm, respectively. The base of the parallelogram so formed is 10 cm.

In the following figure, triangles are formed by joining the vertices of the square as shown. Triangle BEH is an isosceles triangle with its base as one of the sides of the square. Similarly, triangle BAE is also an isosceles triangle as shown in the figure. Also, triangle BAE is congruent to other three triangles which have one of their vertices as that of the square; and similarly, triangle BEH is congruent to other three triangles which have one of their sides as that of the square. Find the area of the given figure. (Take = 4.58)

The area of a rectangle ABCD is 48 cm² and its perimeter is 28 cm with AB as the largest side. E and F are the mid-points of AB and DA, respectively. G is a point on CD such that an isosceles triangle EFG is formed in which FG = GE. Find the area of the ΔFEG, if length GF = 6.5 cm.

Take:

State T for true and F for false.

(i) Rohit is making a triangular design piece from a sheet. Two of the sides of the sheet are 16 cm each. The perimeter of the sheet is 50 cm. Thus, he will need 218.8 cm² of the sheet.

(ii) Rajiv's mother is preparing paranthas for him in the shape of triangle. The sides of a parantha are 12 cm, 8 cm and 6 cm. She has ghee to apply on 96 cm². Thus, she can apply ghee on 4 paranthas.

(iii) The sides of a quadrilateral are AB = BC = 20 cm, AD = 30 cm, CD = 18 cm and BD = 30 cm. Its area will be 649 cm².

(iv) We can find the area of a triangle by only knowing its perimeter.

In the given figure, the central square is of side 8 cm and the area of triangles ABC and GEF are equal. If AF divides quadrilateral ABCD as well as triangle GEF into two equal triangles, find the total area of the given shape which is to be put on a flag after the square shaped region from the quadrilateral formed by ABCD has been cut out. (Figure not drawn to scale)