Advertisements
Advertisements
Question
Using Heron’s formula, find the area of a triangle whose sides are 10 cm, 24 cm, 26 cm
Advertisements
Solution
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
RELATED QUESTIONS
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.
Find the area of the triangle formed by the points
(–10, –4), (–8, –1) and (–3, –5)
A triangular shaped glass with vertices at A(– 5, – 4), B(1, 6) and C(7, – 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied
Find the area of triangle AGF
The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, −2). The third vertex is (x, y) where y = x + 3. Find the coordinates of the third vertex.
The sides of the triangular ground are 22 m, 120 m and 122 m. Find the area and cost of levelling the ground at the rate of ₹ 20 per m2
Find the area of an equilateral triangle whose perimeter is 180 cm
The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.
