Advertisements
Advertisements
Question
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Advertisements
Solution
Let the sides of an isosceles triangle be a = 12 cm, b = 12 cm, c = x cm
Since the perimeter of the triangle = 30 cm
∴ 12 cm + 12 cm + x cm = 30 cm
⇒ x = (30 − 24) = 6
Now, semi-perimeter, s = `30/2` cm = 15 cm
∴ Area of the triangle = `sqrt(s(s - a)(s - b)(s - c))`
= `sqrt(15(15-12)(15-12)(15-6)) cm^2`
= `sqrt(15 xx 3 xx 3 xx 9) cm^2`
= `sqrt(15 xx 3 xx 3 xx 3 xx 3 xx 3) cm^2`
= `sqrt(3^2 xx 3^2 xx 3 xx 5) cm^2`
= `3 xx 3 xx sqrt(3 xx 5) cm^2`
= `9sqrt15 cm^2`
Thus, the required area of the triangle is `9sqrt15 cm^2`.
APPEARS IN
RELATED QUESTIONS
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.
Find the areas of the given plot. (All measures are in metres.)
Find the area of the triangle formed by the points
(1, – 1), (– 4, 6) and (– 3, – 5)
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
Find the area of triangle FED
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.
An advertisement board is in the form of an isosceles triangle with perimeter 36 m and each of the equal sides are 13 m. Find the cost of painting it at ₹ 17.50 per square metre.
The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per m2 is Rs 918.
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
