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
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
Find the area of the shaded region in the given figure.
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.
Sides of a triangle are cm 45 cm, 39 cm and 42 cm, find its area.
Find the area of the triangle formed by the points
(–10, –4), (–8, –1) and (–3, –5)
If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is
The area of the isosceles triangle is `5/4 sqrt(11)` cm2, if the perimeter is 11 cm and the base is 5 cm.
If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm2.
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 design is made on a rectangular tile of dimensions 50 cm × 70 cm as shown in the following figure. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tile.
