Analyzing the Triangle Geometry
The question asks for the area of a triangle with a given base and two equal side lengths. This describes an isosceles triangle.
- Base ($b$): 10 cm
- Equal Sides ($s$): 6 cm
The area of a triangle is calculated using the formula:
$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $
We need to find the height ($h$) of the triangle.
Calculating the Triangle Height
In an isosceles triangle, the altitude drawn to the base bisects the base.
- The base is divided into two segments, each of length $\frac{10}{2} = 5$ cm.
- The altitude forms a right-angled triangle with one of the equal sides (hypotenuse = 6 cm) and half the base (one leg = 5 cm). The altitude is the other leg.
Using the Pythagorean theorem ($a^2 + b^2 = c^2$):
$ 5^2 + h^2 = 6^2 $
$ 25 + h^2 = 36 $
$ h^2 = 36 - 25 $
$ h^2 = 11 $
$ h = \sqrt{11} \text{ cm} $
Calculating the Triangle Area
Now, substitute the base and the calculated height into the area formula:
$ \text{Area} = \frac{1}{2} \times b \times h $
$ \text{Area} = \frac{1}{2} \times 10 \text{ cm} \times \sqrt{11} \text{ cm} $
$ \text{Area} = 5 \times \sqrt{11} \text{ sq. cm} $
The area of the triangle is $5\sqrt{11}$ sq. cm.
Similar Questions
- It is given that, \(\Delta ABC \sim \Delta EDF\) such that \(AB = 5 \text{ cm}\), \(AC = 7.5 \text{ cm}\), \(DF = 15 \text{ cm}\) and \(ED = 12.5 \text{ cm}\). The sum of the remaining sides of the triangles is:
In two triangles, ∆ABC ∼ ∆PQR, AB=12cm and PQ=4cm, if AL and PM are altitudes of the respected triangles, then what will be AL : PM?
In the given figure, if \(RS = 3\sqrt{3} \text{ cm}\) and \(RPS\) is an equilateral triangle, then find the value of \(QR\)
- In a right angled triangle, with angle at \(A\) being \(90^\circ\), the side \(AB\) is of length 3cm and \(BC\) is 12 cm. What is the length of side \(AC\)?
For a pair of similar triangles shown in the figure, the angles made at $B$ and $R$ are same in both the triangles $BAC$ and $RAQ$. If the ratio of the areas of the two triangles is 2:1, and if the area of $BAC$ is $100\text{ cm}^2$ then what is the area of $RAQ$ in sq.cm.?
- In a triangle $ABC$, the length of the side $AB$ is 2m, the angle at $C$ is $60^\circ$ and the angle at $B$ is $30^\circ$, what is the length of side $AC$?
In a right angled triangle, with angle at A being , the side $AB$ is of length 4cm and $BC$ is 15 cm. What is the length of side $AC$?
- Triangles $PQR$ and $ABC$ are similar triangles.
Triangle $ABC$ have the following sides.
$AB = 36\text{ cm}$
$AC = 20\text{ cm}$
$BC = 48\text{ cm}$
Triangle $PQR$ have the following sides:
$PQ = 9\text{ cm}$
$PR = 5\text{ cm}$
What is the length of side $RQ$ =? What is the angle at $B$ in the triangle $ABC$, if the angle made at $K$ is $30^\circ$ and the triangles shown in the figure are similar?
- In a triangle the length of the sides, $AB$ is 3m and $BC$ is 5m what is the length of $AC$, if the angle formed at $B$ is $60^\circ$
Important Questions from Triangles
Among the following options, which are NOT sides of a triangle?
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
In the equilateral Δ ABC, the base BC is trisected at D and E. The line through D, Parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. If EG and DF intersect at H, then what is the ratio of the sum of the area of parallelogram AGHF and the area of the Δ DHE to the area of the Δ ABC?
The product of the perimeter of a triangle, the radius of its in‐circle, and a number gives the area of the triangle. The number is
A man goes 24 m towards east and then 10 m towards north. How far is he away from his initial position?
