Question 1: Find the area, of the triangle, having:

(i) base , height

(ii) base , height

(iii) base , height

(iv) base , height

Answer:

(i) Area of a triangle

(ii) Area of a triangle

(iii) Area of a triangle

*Note: *

(iv) Area of a triangle

*Note: *

Question 2: Find the height of the triangle whose:

(i) area , base

(ii) area , base

Answer:

(i) Height

(ii) Height

Question 3: Find the base of the triangle whose:

(i) area , height

(ii) area , height

Answer:

(i) Base

(ii) Base

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

Height

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

Height

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

Height

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 Base and Height

Area of a triangle

Therefore Base and Height

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

Height

(ii)

Area of triangle

Therefore Area of triangle

Height

(iii)

Area of triangle

Therefore Area of triangle

Height

Question 10: Find the area of a right triangle whose hypotenuse is long and one of the sides containing the right-angle measures .

Answer:

height

Area of a triangle

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, height

Base

Question 12: The legs of a right triangle are in the ratio and its area is . Find its hypotenuse.

Answer:

Let the Base and Height

Area of a triangle

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 base

Base

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