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### High School Mathematics12.48 Important Points - Areas

 1. The union of triangle and its interior is called the triangular region. 2. The union of a quadrilateral and its interior is called the quadrilateral region. 3. A polygonal region is the union of a polygon and its interior. 4. To every polygonal region, there corresponds a unique positive real number called its area. 5. Congruent triangles have the same area. 6. A diagonal of a parallelogram divides it into two congruent triangles. 7. Area of a parallelogram = base * corresponding altitude = bh. 8. Parallelograms on the equal bases and between the same parallel lines are equal in area. 9. Triangle on the same base and between the same parallel lines are equal in area. 10. Area of a triangle = 1/2 * base * altitude = 1/2*bh. 11. If a triangle and a parallelogram are on the same base and between the same parallel lines, then the area of the triangle is equal to half the area of the parallelogram. 12. Area of trapezium = 1/2*height*sum of parallel sides = 1/2*h(a+b). 13. If two triangles have the same area and their bases are equal, then the corresponding altitudes are equal. 14. Area of a quadrilateral = 1/2*diagonal*sum of offsets on it = 1/2*d(h1 + h2). 15. If the diagonals of a quadrilateral are perpendicular to each other then its area = 1/2*d1d2, where d1 and d2 are the diagonals. 16. Area of rhombus = 1/2 * product of diagonals = 1/2*d1d2. 17. A median divides a triangle into two triangles of equal areas. 18. If D, E, F are the mid points of the sides of a triangle, then triangle DEF = 1/4 triangle ABC. 19. If a rectangle and a parallelogram have the same base and are between the same parallel lines, then their areas are equal. 20. If a rectangle and a triangle have the same base and are between the same parallel lines, then the area of the triangle is half the area of the rectangle. Directions: Choose the correct answer.
 Q 1: ABCD is a rectangle with length lcm and breadth bcm then area of ABCD = ______.(l+b) Sq. cm.lm Sq. cm. Q 2: The diagonal of a parallelogram divides it into two triangles of ______ area.differentequal Q 3: If a triangle and a parallelogram are on the same base and between the parallel lines, the area of the triangle is _______ to half of the parallelogram.not equalequal Q 4: The area of a parallelogram is the product of any of its sides and the corresponding ______.diagonalaltitude Q 5: Any side of a parallelogram can be taken as ________.basediagonal Q 6: Area of a triangle is half the ______ of any of its sides and the corresponding altitude.differentsumproduct Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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