CBSE Class 9 Mathematics Area Of Triangles Herons Formula Worksheet Set A

Question. The perimeter of an equilateral triangle is 60 m, then its area is:
(a) 10√3m²
(b) 15√3m²
(c) 20√3m²
(d) 100√3m²

Answer: D

Question. The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is
(A) 1322 cm²
(B) 1311 cm²
(C) 1344 cm²
(D) 1392 cm²

Answer: C

Question. An isosceles right triangle has area 8 cm². The length of its hypotenuse is
(a) √32cm
(b) √16cm
(c) √48cm
(d) √24cm

Answer: A

Question. The length of each side of an equilateral triangle having an area of 9√3cm² is
(A) 8 cm
(B) 36 cm
(C) 4 cm
(D) 6 cm

Answer: D

Question. If the area of an equilateral triangle is 16√3cm² then the perimeter of the triangle is
(A) 48 cm
(B) 24 cm
(C) 12 cm
(D) 36 cm

Answer: B

Question. The area of an equilateral triangle with side 2√3cm is
(a) 5.196 cm²
(b) 0.886 cm²
(c) 3.496 cm²
(d) 1.732 cm²

Answer: A

Question. The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of its longest altitude
(a) 16√5cm
(b) 10√5cm
(c) 24√5cm
(d) 28 cm

Answer: C

Question. The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 9 paise per cm² is
(A) Rs2.00
(B) Rs2.16
(C) Rs2.48
(D) Rs3.00

Answer: B

Question. The base and the corresponding altitude of a parallelogram are 10 cm and 3.5 cm, respectively. The area of the parallelogram is 30 cm².
Answer. The base of the parallelogram is 10 cm and the corresponding altitude is 3.5 cm.
Area of || gm = base × corresponding altitude.
= 10 cm × 3.5 cm = 35 cm².
Hence, the given statement is false.

Question. The area of a triangle with base 4 cm and height 6 cm is 24 cm².
Answer. Area of Δ = 1/2 X base X height = 1/2 X 4X 6 = 12cm²
Hence, the statement is false.

Question. The area of the equilateral triangle is 20√3cm² whose each side is 8 cm.
Answer. Area of equilateral = √3/4 (side)²
= √3/4 (8)² = √3/4 X 64 = 16 √3cm²
Hence, the given statement is false.

Question. The area of a trapezium is 475 cm2 and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other.
Answer. Area of trapezium = 1/2 × (Sum of the parallel side) × height
⇒ 475 = 1/2 x (x + x + 4) x 19cm
⇒ 2x + 4 = 950/19 = 50
⇒ 2x + 50 - 4 = 46, x = 46 ÷ 2 = 23
Hence, the length of two parallel sides are 23 cm and (23 + 4) cm i.e., 23 cm and 27 cm.

Question. A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.
Answer. The length of the rectangular plot = 40 m
And the breath of the plot = 15 m.
As a minimum of 3 m wide space should be left in the front and back 2 m wide space each
of other side, so the largest area where the house can be constructed.
= [40 − 2(3)] [15− 2(2)] = 34 × 11 = 374m²