Question

Construct an isosceles triangle whose base is $6cm$ and altitude $3cm$ and then find the area of triangle

• A. $9c{m}^2$
• B. $18c{m}^2$
• C. $24c{m}^2$
• D. $36c{m}^2$

Answer 1

The correct option is A $9c{m}^2$

1. Mark a point B that will be one vertex of the new triangle.
2. Set the compasses' width to 6 cm, the length of the segment BC.
3. With the compasses' point on B, make an arc near the future vertex C of the triangle.
4. Mark a point C on this arc. This will become the next vertex of the new triangle. Join B and C.
5. To ocnstruct the perpendicular bisector of BC, place the compasses on one end of the line segment. Set the compasses' width to a approximately two thirds the line length. The actual width does not matter.
6. Without changing the compasses' width, draw an arc above and below the line.
7. Again without changing the compasses' width, place the compasses' point on the the other end of the line. Draw an arc above and below the line so that the arcs cross the first two.
8. Using a straightedge, draw a line between the points where the arcs intersect. This line is perpendicular to the first line and bisects it.
9. Set the compasses' width to the distance from A to B. This is the desired altitude of the triangle = 3 cm.
10. Place the point of the compasses on the midpoint of the base line, and draw an arc across the perpendicular drawn earlier. This is the third vertex A, of the triangle.
11. Draw the two side lines AB and AC. This is an isosceles triangle ABC.
base of given triangle = $6cm$ and height=$3cm$

area of triangle = $\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times 3\times 6=9c{m}^2$