Identify Triangle Type Using Sides
We are given the sides of a triangle: 44 cm, 33 cm, and 55 cm. To find the area efficiently, let's first determine if it's a special type of triangle, like a right-angled triangle. We can use the Pythagorean theorem ($a^2 + b^2 = c^2$) for this check.
- Assign the sides: Let $a = 33$ cm, $b = 44$ cm, and $c = 55$ cm. The longest side ($c$) is the potential hypotenuse.
- Calculate the squares of the two shorter sides:
- $a^2 = 33^2 = 1089$
- $b^2 = 44^2 = 1936$
- Calculate the square of the longest side:
- $c^2 = 55^2 = 3025$
- Check if the Pythagorean theorem holds: $a^2 + b^2 = 1089 + 1936 = 3025$.
- Compare: Since $a^2 + b^2$ equals $c^2$ ($3025 = 3025$), the triangle is a right-angled triangle.
Calculate Triangle Area
The area of a right-angled triangle is given by the formula:
$Area = 1/2 * base * height$
In a right-angled triangle, the two shorter sides (legs) serve as the base and height.
- Identify base and height: The base and height are 33 cm and 44 cm.
- Substitute the values into the area formula: $Area = 1/2 * 33 cm * 44 cm$
- Perform the calculation: $Area = 33 cm * (44 cm / 2)$
- Simplify: $Area = 33 cm * 22 cm$
- Final result: $Area = 726 cm$^2$
Therefore, the area of the triangle is 726 cm$^2$.
Similar Questions
- In $\triangle ABC$, $BD \perp AC$ at $D$ and $\angle DBC = 40^\circ$. $E$ is a point on $BC$ such that $\angle CAE = 37^\circ$. What is the measure of $\angle AEB$?
- In $\Delta ABC$, $BD \perp AC$ at D and $\angle DBC = 71^\circ$. E is a point on BC such that $\angle CAE = 17^\circ$. What is the measure of $\angle AEB$?
- In triangle ABC, bisector of $\angle\text{ABC}$ and $\angle\text{ACB}$ meet at O. If $\angle\text{BAC} = 60^\circ$, then find the measure of $\angle\text{BOC}$.
- In $\Delta\text{XYZ}$, $\text{XY} = 12\text{ cm}$ and $\text{YZ} = 18\text{ cm}$. $\text{XW}$, the angle bisector of $\text{YXZ}$, meets $\text{YZ}$ at $\text{W}$, such that $\text{YW} : \text{WZ}$ is $4 : 5$. Find the length of the third side of the triangle.
- In $\Delta\text{PQR}$, $\text{QR}$ is extended up to $\text{S}$ so that $\text{RS} = \text{RP}$. If $\angle\text{PRQ} = 70^\circ$ and $\angle\text{QPS} = 110^\circ$ then find the measure of $\angle\text{PQS}$.
- The areas of two similar triangles are respectively $16\text{ m}^{2}$ and $36\text{ m}^{2}$. Find the ratio of their corresponding sides.
- In $\Delta PQR$, QR is extended up to S, so that RS = RP. If $\angle RPQ = 55^\circ$ and $\angle PRS = 110^\circ$, then find the measure of $\angle PQS$.
- The perimeter of an equilateral triangle ABC is 22.2 cm. What is the area of triangle (in $cm^2$)?
- In $\triangle\text{ABC}$, $\text{BD} \perp \text{AC}$ at $\text{D}$ and $\angle\text{DBC} = 60^{\circ}$. $\text{E}$ is a point on $\text{BC}$ such that $\angle\text{CAE} = 20^{\circ}$. What is the measure of $\angle\text{AEB}$?
- In a triangle, if angle $A = 30^\circ$ and angle $B = 45^\circ$, then what is the angle of C?
Important Questions from Triangles
What is the circumcenter of the triangle ABC?
What is the centroid of the triangle ABC?
What is the foot of the altitude from the vertex A of the triangle ABC?
In ΔABC, D is a point on BC such that ∠ADB = 2∠DAC, ∠BAC = 70° and ∠B = 56°. What is the measure of ∠ADC?
In ΔABC, ∠A = 66° and ∠B = 50 °. If the bisectors of ∠B and ∠C meet at P, then ∠BPC – ∠PCA = ?
