Question

if the sides that form the right angle of a triangle are 3.5cm and 4.2cm long find the area of the triangle​

Answer 1

Answer:

7.35 cm²

Step-by-step explanation:

As per the provided information in the given question, we have :

• Sides that form the right angle of a triangle are 3.5cm and 4.2cm long.

We are asked to calculate the area of the triangle.

Take a look at the figure provided in the attachment. a and b are the two sides which are forming right angle of the triangle. Side a can be considered as height or altitude and side b can be considered as the base of the triangle.

We know that,

$\longmapsto\bf {Area_{(\Delta)} = \dfrac{1}{2} \times b \times h }$

• b denotes base
• h denotes height

$\longmapsto\rm {Area_{(\Delta)} = \dfrac{1}{2} \times a \times b }$

Substitute the values.

$\longmapsto\rm {Area_{(\Delta)} = \Bigg ( \dfrac{1}{2} \times 3.5 \times 4.2 \Bigg ) \; cm^2 }$

Simplifying further.

$\longmapsto\rm {Area_{(\Delta)} = \Bigg ( \dfrac{1}{2} \times \dfrac{35}{10} \times \dfrac{42}{10} \Bigg ) \; cm^2 }$

Divided 42 by 2.

$\longmapsto\rm {Area_{(\Delta)} = \Bigg (1 \times \dfrac{35}{10} \times \dfrac{21}{10} \Bigg ) \; cm^2 }$

Multiplying 35 with 21 and 10 with 10.

$\longmapsto\rm {Area_{(\Delta)} = \Bigg ( \dfrac{735}{100} \Bigg ) \; cm^2 }$

Dividing 735 with 100.

$\longmapsto\bf {Area_{(\Delta)} = 7.35 \; cm^2 }$

∴ Area of the triangle is 7.35 cm².

$\rule{200}2$

More Information :

Points about triangles :

• Sum of interior angles of a triangle = 180°
• Sum of two interior opposite angles = Exterior angle
• Area of triangle = $\sf { \dfrac{1}{2} \times b \times h }$
• Perimeter of triangle = Sum of all sides

Area of a triangle when its sides are given :

$\longmapsto \rm { \sqrt{s (s-a)(s-b)(s-c)} }$

Where,

s = $\rm {\dfrac{a+b+c}{2} }$