ABC is a triqngle rightangled at B with AB =14cm and BC=24cm with the vertices A,B andC centres arcs are drawn each of radius 7cm find the area of the left over region of the triangle
Answers
Answer:
52.5 cm^2
Step-by-step explanation:
ABC is a right angled triangle, Angle B = 90°
AB = 14cm
BC = 24cm
Using Pythagorean theorem
AC = √AB^2+BC^2
= √14^2+24^2
= √196+576
= √772
= √4×193
= 2√193 cm
Now,
Area of the Triangle ABC = 1/2 ×base ×height
= 24×14 / 2
= 24×7
= 168 cm^2
Given that,
With the vertices A,B andC centre arcs are drawn each of radius 7cm.
Therefore 3 arcs each of radius 7cm are formed
The area covered by these arcs will be equal to 3/4th the area of circle with radius 7cm
Area covered by 3 arcs = 3/4 πr^2
= 3×22×7×7 / 7×4
= 3×7×11 /2
= 231/2
= 115.5 cm^2
Area of left over region of the triangle = 168-115.5
=52.5cm^2
Hope it helps.