Geometry: Area of Triangles Problems

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What is the formula for calculating the area of a triangle according to Heron?

Area of a triangle = s( s - a )( s - b )( s - c )

What does s represent in Heron's formula for the area of a triangle?

Semi-perimeter, half the perimeter of the triangle

How is the semi-perimeter (s) of a triangle calculated?

s = a + b + c / 2

What is the condition for using Heron's formula instead of finding the height of a triangle?

When it is not possible to find the height of the triangle easily Signup and view all the answers

In the given example, what are the sides of the triangular park ABC?

a = 40 m, b = 24 m, c = 32 m Signup and view all the answers

What shape do the sides of the park form, and what is the largest side of the park?

The sides form a right triangle, with BC as the hypotenuse (40 m) Signup and view all the answers

What is the area of the wall painted with the message 'KEEP THE PARK GREEN AND CLEAN' if the sides of the wall are 15m, 11m, and 6m?

The area painted in colour is 33 sq. m. Signup and view all the answers

Calculate the area of a triangle with sides 18cm, 10cm, and a perimeter of 42cm.

The area of the triangle is 72 sq. cm. Signup and view all the answers

A triangle has sides in the ratio of 12:17:25 and a perimeter of 540cm. Determine its area.

The area of the triangle is 4392 sq. cm. Signup and view all the answers

Given an isosceles triangle with a perimeter of 30cm and equal sides of 12cm, what is the area of the triangle?

The area of the triangle is 72 sq. cm. Signup and view all the answers

How can a farmer calculate wages for labourers based on the area cultivated per square metre in a quadrilateral field?

The farmer can divide the quadrilateral field into triangular parts and use the formula for the area of a triangle. Signup and view all the answers

In Kamla's fields, one triangular field had sides of 240m, 200m, and 360m, and the adjacent field had sides 240m, 320m, and 400m. How did she divide these fields for planting different crops?

She joined the mid-point of the longest side to the opposite vertex to divide the field into two parts. Signup and view all the answers

How can you find the area of a scalene triangle when you know the lengths of its sides but not its height?

You can use Heron's Formula to calculate the area of a scalene triangle when you know the lengths of its sides. Signup and view all the answers

Who is Heron and what is he famous for?

Heron was a mathematician born around 10 AD in Alexandria, Egypt. He is famous for deriving the formula for the area of a triangle in terms of its three sides. Signup and view all the answers

What did Heron's Book I focus on in terms of geometrical works?

Book I of Heron's works focused on the area of squares, rectangles, triangles, trapezoids, regular polygons, circles, and surfaces of cylinders, cones, and spheres. Signup and view all the answers

Explain the significance of the perpendicular XP in the given text.

The perpendicular XP divides the base of the triangle into two equal parts and helps in calculating the area using the Pythagorean theorem. Signup and view all the answers

How did Heron contribute to the field of mathematics?

Heron made significant contributions to applied mathematics, particularly in the area of mensuration and geometry. Signup and view all the answers

What is the significance of Heron's Formula in calculating the area of a triangle?

Heron's Formula is important as it allows the calculation of the area of a triangle based on the lengths of its three sides, without requiring the height. Signup and view all the answers