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 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 = ?
In a triangle ABC, points P and Q are on AB and AC, respectively, such that AP = 4 cm, PB = 6 cm, AQ = 5 cm and QC = 7.5 cm. If PQ = 6 cm, then find BC (in cm).
The perimeters of two similar ΔABC and Δ PQR are 48.4 cm and 12.1 cm, respectively. What is the ratio of the areas of Δ ABC and Δ PQR?
