Advertisements
Advertisements
प्रश्न
Using Heron’s formula, find the area of a triangle whose sides are 10 cm, 24 cm, 26 cm
Advertisements
उत्तर
Let a = 10 cm, b = 24 cm and c = 26 cm
s = `("a" + "b" + "c")/2`
= `(10 + 24 + 26)/2`
s = `60/2`
= 30 cm
s – a = 30 – 10 = 20 cm
s – b = 30 – 24 = 6 cm
s – c = 30 – 26 = 4 cm
Area of a triangle
= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`
= `sqrt(30 xx 20 xx 6 xx 4)`
= `sqrt(2 xx 3 xx 5 xx 2^2 xx 5 xx 2 xx 3 xx 2^2)`
= `sqrt(2^6 xx 3^2 xx 5^2)`
= 23 × 3 × 5
= 8 × 3 × 5
= 120 cm2
Area of a triangle = 120 cm2
APPEARS IN
संबंधित प्रश्न
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
The perimeter of a triangle is 300 m. If its sides are in the ratio 3 : 5 : 7. Find the area of the triangle ?
Find the area of a quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA =34 cm and diagonal BD =20 cm.
The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
The area of triangle formed by the points (− 5, 0), (0, – 5) and (5, 0) is
If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm2.
A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Find the area of the parallelogram.
The perimeter of a triangular field is 420 m and its sides are in the ratio 6 : 7 : 8. Find the area of the triangular field.
A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1 m2 of the field, find the total cost of ploughing the field.
