Heron's Formula quiz

The semi-perimeter of a triangle with sides 5 cm, 12 cm and 13 cm is:

The area of the triangle with sides 5 cm, 12 cm and 13 cm is:

Heron's formula was given by Heron of:

The area of an equilateral triangle of side 6 cm is:

If the sides of a triangle are 3 cm, 4 cm and 5 cm, then s - 3 equals:

The area of a triangle with sides 7 cm, 24 cm and 25 cm is:

The perimeter of an equilateral triangle is 30 cm. Its semi-perimeter is:

The area of an isosceles triangle with sides 5 cm, 5 cm and 6 cm is:

To find the area of a quadrilateral using Heron's formula, we divide it into:

The sides of a triangle are 9 cm, 10 cm and 17 cm. Its semi-perimeter is:

Find the area of a triangle with sides 9 cm, 10 cm and 17 cm. (2 marks)

Find the area of an equilateral triangle of perimeter 24 cm, in terms of the square root of 3. (2 marks)

Find the area of a triangle with sides 6 cm, 8 cm and 10 cm using Heron's formula. (2 marks)

The sides of a triangle are 11 m, 60 m and 61 m. Find its semi-perimeter and area. (2 marks)

Show that Heron's formula for an equilateral triangle of side x gives the area as the square root of 3 times x^2 divided by 4. (2 marks)

Find the area of an isosceles triangle with base 10 cm and equal sides 13 cm each. (2 marks)

The area of a triangle with sides 20 cm, 21 cm and 29 cm is 210 sq cm. Find the height corresponding to the longest side, correct to two decimal places. (2 marks)

The sides of a triangle are 35 cm, 54 cm and 61 cm. Find its semi-perimeter. (2 marks)

Find the area of a rhombus whose side is 5 cm and one diagonal is 8 cm. (2 marks)

Why can a triangle not have sides 3 cm, 4 cm and 8 cm? What happens if you try Heron's formula? (2 marks)

The sides of a triangular plot are in the ratio 5 : 12 : 13 and its perimeter is 300 m. Find its area. (3 marks)

A triangular board has sides 15 cm, 20 cm and 25 cm. Find its area and the cost of painting it at Rs 2 per sq cm. (3 marks)

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm. Give the answer correct to two decimal places, taking the square root of 4851 as 69.65. (3 marks)

A quadrilateral ABCD has AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm. Find its area, taking the square root of 21 as 4.58. (3 marks)

An isosceles triangle has perimeter 32 cm and each equal side is 10 cm. Find the base and its area. (3 marks)

Read the passage and answer the questions. A traffic signboard is an equilateral triangle with side 60 cm. The words SCHOOL AHEAD are painted on it. (i) Find the semi-perimeter of the board. (ii) Find its area, in terms of the square root of 3. (iii) If the square root of 3 is taken as 1.73, find the area to the nearest sq cm. (5 marks)

Read the passage and answer the questions. A farmer has a triangular field with sides 50 m, 120 m and 130 m. He wants to grow wheat and needs to know the area to buy seeds. (i) Find the semi-perimeter of the field. (ii) Find its area. (iii) If seeds cost Rs 3 per square m, find the total cost. (5 marks)

Read the passage and answer the questions. A park in the shape of a quadrilateral ABCD has AB = 9 m, BC = 12 m, CD = 5 m, AD = 8 m and angle C = 90 degrees. The diagonal BD divides it into two triangles. (i) Find the length of BD. (ii) Find the area of triangle BCD. (iii) Find the area of triangle ABD using Heron's formula, taking the square root of 35 as 5.92, and hence the total area. (5 marks)

Read the passage and answer the questions. A kite is made of two triangular sheets of paper. One is an isosceles triangle with equal sides 6 cm and base 8 cm, and the other has sides 10 cm, 10 cm and 8 cm, sharing the base of 8 cm. (i) Find the area of the smaller triangle, taking the square root of 5 as 2.24. (ii) Find the area of the larger triangle, taking the square root of 21 as 4.58. (iii) Find the total area of paper. (5 marks)

Read the passage and answer the questions. A company advertises on the triangular side walls of a flyover. Each wall has sides 122 m, 22 m and 120 m, and the rent is Rs 5000 per square m per year. (i) Find the area of one wall. (ii) Find the rent for one wall for 3 months. (iii) Is the wall a right triangle? Justify. (5 marks)

Draw a rough figure and find the area of a quadrilateral PQRS with PQ = 9 cm, QR = 40 cm, RS = 28 cm, SP = 15 cm and PR = 41 cm. Explain each step. (6 marks)

A triangular park has sides 120 m, 80 m and 50 m. A gardener has to put a fence all around it and plant grass inside. Find the area to be planted, leaving the answer in terms of a square root, and the cost of fencing at Rs 20 per metre leaving a 3 m wide gate. (6 marks)

Draw a rough sketch of a triangle with sides 26 cm, 28 cm and 30 cm. Find its area by Heron's formula, and then find the length of the altitude on the side of 28 cm. (6 marks)

A rhombus-shaped field has each side 30 m and its longer diagonal 48 m. Draw a rough figure and find its area using Heron's formula on the two triangles. If each of 18 cows is given an equal part to graze, how much area does each get? (6 marks)

Derive the formula for the area of an equilateral triangle of side x using Heron's formula. Use it to find the area of a hexagon of side 4 cm made of six equilateral triangles, in terms of the square root of 3. (6 marks)