Question 1: Find the area, of the triangle, having:
i) ,
ii)
,
iii) ,
iv)
,
Answer:
i)
ii)
iii)
Note:
iv)
Note:
Question 2: Find the height of the triangle whose:
i) ,
ii)
,
Answer:
i)
ii)
Question 3: Find the base of the triangle whose:
i) ,
ii)
,
Answer:
i)
ii)
Question 4: Find the area of the triangle whose sides are and
. Also find the altitude of the triangle corresponding to the largest side.
Answer:
Area of triangle
Therefore Area of triangle
Question 5: Find the area of the triangle whose sides are and
. Find the height of the triangle corresponding to the side measuring
.
Answer:
Area of triangle
Therefore Area of triangle
Question 6: Find the area of a triangular field whose sides are and
. Find the altitude of the triangle corresponding to the smallest side.
Answer:
Area of triangle
Therefore Area of triangle
Question 7: Find the area of an isosceles triangle in which each of the equal sides measures and the third side is
long.
Answer:
Area of triangle
Therefore Area of triangle
Question 8: The base and the height of a triangle are in the ratio and its area is
. Find the base and the height of the triangle.
Answer:
Let the and
Therefore and
Question 9: Find. the area and the height of an equilateral triangle whose each side measures: (i) (ii)
(iii)
(Take
in each case)
Answer:
i)
Area of triangle
Therefore Area of triangle
ii)
Area of triangle
Therefore Area of triangle
iii)
Area of triangle
Therefore Area of triangle
Question 10: Find the area of a right triangle whose hypotenuse is long and one of the sides containing the right-angle measures
.
Answer:
Question 11: The area of a right triangle is and one of its legs is
long. Find the length of the other leg.
Answer:
Let us say,
Question 12: The legs of a right triangle are in the ratio and its area is
. Find its hypotenuse.
Answer:
Let the and
Therefore Hypotenuse
Question 13: The sides of a triangle are in the ratio and its perimeter is
. Find the area of the triangle.
Answer:
Let the sides be , and
Therefore
Hence the sides are and
Question 14: The base of an isosceles triangle is and its perimeter is
. Find its area.
Answer:
Let the side of the isosceles triangle be
Therefore
Area of triangle
Therefore Area of triangle
Question 15: The cost of painting the top surface of a triangular board at paisa per square meter is
. If the height of the board measures
, find its base.
Answer:
Area of the triangular
Question 16: Calculate the area of the quadrilateral in which
and
. (Take
)
Answer:
Area of
For
Therefore Area of
Therefore the area of quadrilateral
Question 17: Calculate the area of the quadrilateral shown in the adjoining figure, it being given that
and
Answer:
In
Area of
Area of
Hence the area of quadrilateral
Question 18: Find the area of the quadrilateral whose diagonal
is
long and the lengths of the perpendiculars from the opposite vertices
and
on
are
and
.
Answer:
Area of
Area of
Hence the area of quadrilateral
Question 19: Find the area of the quadrilateral , given in the adjoining figure in which
and
Answer:
For
Area of triangle
Therefore Area of
For
Area of triangle
Therefore Area of
Hence the area of quadrilateral