Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Find the area of triangle ABC with A (1, –4) and the mid-points of sides through A being (2, –1) and (0, –1).  

Find the area of triangle ABC with A (1, –4) and the mid-points of sides through A being (2, –1) and (0, –1).

 

Answers (1)

Given: A (1, –4) and the midpoint of AB and AC are D(2, –1) and E(0, –1) respectively.

\\ Ar (\triangle ADE ) = \frac{1}{2}\left[x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right) +x_{3}\left(y_{1}-y_2\right) \right] \\\\ \\ Ar (\triangle ADE ) = \frac{1}{2}\left[1\left(-1-(-1)\right)+{2}\left((-1)-(-4)\right) +0\left((-4)-(-1)\right) \right] \\\\ = \frac{1}{2} \times 6 \\\\=3$ Square unit$ \\\\ \frac{Ar (\triangle ABC)}{Ar (\triangle ADE)} = 4 \\ Ar (\triangle ABC)= 4 \times Ar (\triangle ADE) \\\\ = 12 $ Square unit$\\

Steps of construction are:-

(i) Firstly draw a line segment AB of length 4 cm.

(ii) Now cut an arc of radius 5 cm from point A and an arc of 3 cm from point B.

(iii) Name the point of intersection of arcs to be point C.

(iv) Now join point AC and BC. Thus  ABC is the required triangle.

(v) Draw a line AD which makes an acute angle with AB and is opposite of vertex C.

(vi) Cut five equal parts of line AD namely AA 1 , AA 2 , AA 3, AA 4,  AA 5

(vii) Now join A 5 to B. Draw a line A 4 B' parallel to A 5 B.

(viii) And then draw a line B'C' parallel to BC.

Hence  AB'C' is the required triangle.

 

Posted by

Safeer PP

View full answer

Similar Questions

Trending Articles/News

anam-khan

Board Exams Date Sheet 2025 Live: RBSE 10th, 12th exams from March 6; CBSE admit card expected by month-end

Latest Question