Question 1
Question: Using Heron's formula find the area of an equilateral triangle whose perimeter is 15 cm.
Answer:
Perimeter = 15 cm
Each side (a) = 5 cm
Question 2
Question: A triangular field with sides 26 m, 28 m, 30 m has to be leveled. If the cost of leveling is Rs.20 per m2. What is the total cost?
Answer: a = 26 m, b = 28 m, c = 30 m
= 7 x 6 x 4 x 2 = 336 m2
Cost of leveling = 336 x 20 = Rs. 6720
Question 3
Question: The perimeter of a triangle is 42 cm. Two of its sides are 14 cm, 19 cm. Find its area.
Answer: The third side = 42 - (14 + 19) = 9 cm
Semi perimeter
Question 4
Question: A wire of length 32 cm is to be bent in the form of an isosceles triangle of base 12 cm. What is the area of the triangle so formed?
Answer:
Let each of the equal sides be 'x' cm 2x + 12 = 32 x = 10 cm
= 48 cm2
Question 5
Question: The sides of a triangle are in the ratio 12:17:25. Its perimeter is 108 m. Find its area.
Answer: Sum of all the sides = 108 m The ratio of sides = 12: 17: 25 12 + 17 + 25 = 54
= 3 x 6 x 5 x 4 = 360 m2
Question 6
Question: A farmer has a triangular plot of land on which he wants to grow carrots and Radish. He puts a separator along the line AD, D being the mid-point of BC. He grows carrots on one part and Radish in the other. What is the area in hectares used for cultivation of carrots?
Answer:
First let us find area of ABC
= 33600 m2
= 3.36 hectares AD is the median of ABC and hence divided the triangle into two parts of equal area. Area used for cultivation of carrots
Question 7
Question: The sides of a triangle are 16 cm, 30 cm, 34 cm. Find its area using Hero's formula. Also find the length of the altitude drawn on the longest side.
Answer:
The longest side = 34 cm Let 'h' be the altitude drawn on the longest side.
17h = 240
Question 8
Question:
This is a sign board. The area between the two triangles has to be pained red. The cost of painting is Rs.3.50/cm2.What is the total cost?
Answer: Area of PQR :
= 300 x 3.87 = 1161 cm2
Area of ABC :
= 290.25 cm2
area to be painted = 1161 - 290.25 = 870.75 cm2
Cost of painting = 870. 75 x 350
= Rs. 3047.63
Question 9
Question:
ABCD is a kite made of colour paper. How many metres of colour paper is required if the width of the paper is 40 cm.
Answer:
Area of ABC:
= 1200 cm2
Area of DBC 
= 4512 cm2Area of the kite = 1200 + 4512 = 5712 cm2
Width of the paper = 40 cm
= 1.428 m
Question 10
Question: The perimeter of rhombus is 48 cm. One of the diagonals is 16 cm. What is its area.
Answer:
Perimeter = 48 cm
Area of ACD : 
Area of the rhombus = 2 x area of the triangle
