ABCD is a rectangle in the diagram. find the area of triangle ABP and triangle ABD
Answers
Question 1.
Draw a triangle of sides 3,4 and 6 centimeters. Draw three different right triangles of the same area.
Answer:
Draw ∆ ABC having sides 3 cm, 4 cm, and 6 cm.
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-1
Draw a line parallel to AB through C and a line from B perpendicular to the parallel line, both lines intersect at point E. Now ∆ABE is a right angled triangle. Also draw a line perpendicular to the parallel line through A, which makes a point Don parallel line, join BD. ∆ ABD is a right angled triangle.
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-2
Similarly make right-angled triangle by drawing line parallel to AC through B, and a line from A perpendicular to the parallel line, both lines intersect at point F.
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-3
The right traingle ∆ DAB, ∆ ABE, ∆ CAF have the same area as that of ∆ ABC.
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Question 2.
Draw the triangle shown below in your notebook. Draw triangles ABP, BCQ and CAR of the same area with measurements given below.
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-4
∠BAP = 90°
∠BCQ = 60°
∠ACR = 30°
Answer:
1.
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-5
Draw a line parallel to AB through C. Draw a perpendicular from A and the point of intersection of perpen-dicular and parallel line is P. Then draw ∆ABP then ∠BAP = 90°. Areas of ∆ABC and ∆ABP are equal.
2.
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-6
Draw a line parallel to BC through A from C make angle 60° both lines intersect at point Q. Then draw ∆ BCQ. Areas of ∆ ABC and ∆ BCQ are equal.
3.
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-7
Draw a line parallel to AC through B from C make angle 30° both lines intersect at point R. Then draw ∆ACR. Areas of ∆ABC and ∆ ACR are equal.
Question 3.
Draw a circle and a triangle with one vertex at the centre of the circle and the other two on the circle. Draw another triangle of the same area with all three vertices on the circle.
Answer:
Draw a line with centre C and AB is the chord of the circle. Draw ∆ ABC then draw a line parallel to AB through C this line touches the circumference at a point D then complete ∆ ABD. Area of ∆ ABC = Area of ∆ ABD
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-8
Question 4.
How many different (non-congruent) triangles can you draw with two sides 8 and 6 centimetres and area 12 square centimetres? What if the area is to be 24 square centimetres?
Answer:
For the triangle of area of 12 sq.cm., the height from the 8 cm side should be 3cm.
Then the area = 12 x 8 x 3 =12 sq.cm
Draw a line 8 cm long. Draw another line parallel to it at a distance of 3 cm. Draw a circle of radius 6 cm with one end of the first line as the center. The points where this circle cuts the second line are the third vertex of the triangle.
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-9
We can draw two triangles ∆ OBC and ∆ OCA having area 12 sq.cm.
For the triangle of area 24 sq cm, the height from the 8 cm side should be 6 cm.
Kerala Syllabus 9th Standard Maths Solutions Chapter 1 Area img-10
We can draw only one triangle of this type.
Answer:
ABCD is a rectangle in the diagram. find the area of triangle ABP and triangle ABD