Question

In ABC, D∈AB so that AD;DB=1 : 3. If ACDB = 12ft2 Find AACD and AABC

Answer 1

Answer:

Area of $\triangle$ACD = 4 $ft^2$

Area of $\triangle$ABC = 16 $ft^2$

Step-by-step explanation:

Given that:

D is a point on AB.

and ABC is a triangle.

AD:DB = 1 : 3

Area of $\triangle$CDB = 12 $ft^2$

Kindly refer to the attached image as per the given dimensions and values.

To find:

Area of $\triangle$ACD and Area of $\triangle$ABC = ?

Solution:

Formula for area of a triangle = $\frac{1}{2}\times Base \times Height$

The altitudes of triangles $\triangle$CDB and $\triangle$ACD are equal in dimensions.

Therefore the area of triangles $\triangle$CDB and $\triangle$ACD will be equal to the ratio of their bases.

Area of $\triangle$ACD : Area of $\triangle$CDB = AD: DB = 1 : 3

$\Rightarrow$ Area of $\triangle$ACD = $\frac{12}{3} = \bold{4 ft^2}$

Area of $\triangle$ABC = Area of $\triangle$ACD + Area of $\triangle$CDB = 12 + 4 = 16 $ft^2$

Therefore, the answer is:

Area of $\triangle$ACD = 4 $ft^2$

Area of $\triangle$ABC = 16 $ft^2$