Find the area of a triangle whose sides measure 8 cm, 10 cm and 12 cm.


A) \( \Large 8\sqrt{63} \)sq cm

B) \( \Large 5\sqrt{63} \)sq cm

C) \( \Large 6\sqrt{53} \)sq cm

D) \( \Large 7\sqrt{93} \)sq cm

Correct Answer:
B) \( \Large 5\sqrt{63} \)sq cm

Description for Correct answer:

Given that,

a=8cm, b = 10 cm and c=12cm

We know, that

s = \( \Large \frac{a+b+c}{2} \) = \( \Large \frac{8+10+12}{2} \)

= \( \Large \frac{30}{2} \)=15cm

(s-a)=(15-8)=7cm

(s-b)=(15-10)=5cm

(s-c)=(15-12)=3cm

Area = \(  \Large \sqrt{s(s-a)(s-b)(s-c)} \)

= \(  \Large \sqrt{15\times 7\times 5\times 3} \)= \(  \Large \sqrt{1575} \)= \(  \Large \sqrt{25\times 63} \)

= \(  \Large 5\sqrt{63} \)sq cm.


Part of solved Area and perimeter questions and answers : >> Elementary Mathematics >> Area and perimeter








Comments

No comments available




Similar Questions
1). The area of a right angled triangle is 40 sq cm. If its base is equal to 28 cm. find its height
A). \( \Large 3\frac{6}{7} \)cm
B). \( \Large 4\frac{6}{7} \)cm
C). \( \Large 2\frac{6}{7} \)cm
D). \( \Large 5\frac{6}{7} \)cm
-- View Answer
2). The three sides of a triangle are 15, 25 and x units. Which one of the following is correct?
A). \( \Large 10 < x < 40 \)
B). \( \Large 10 \le x \le 40 \)
C). \( \Large 10 \le x < 40 \)
D). \( \Large 10 < x \le 40 \)
-- View Answer
3). A triangle with three equal sides has its area equal to \( \Large \Large 3\sqrt{3} \)sq cm. Find its perimeter.
A). \( \Large 6\sqrt{3} \)cm
B). \( \Large 2\sqrt{3} \)cm
C). \( \Large 5\sqrt{3} \)cm
D). \( \Large 7\sqrt{3} \)cm
-- View Answer
4). The sides of a triangle area in the ratio of \( \Large \frac{1}{3}:\frac{1}{4}:\frac{1}{5} \) and its perimeter is 94 Cm.Find the length of the smallest side of the triangle.
A). 18 cm
B). 22.5 cm
C). 24 m
D). 27 cm
-- View Answer
5). The area of an equilateral triangle is \( \Large \Large 4\sqrt{3} \)sq cm. Find the length of each side of the triangle
A). 3 cm
B). \( \Large 2\sqrt{2} \)cm
C). \( \Large 2\sqrt{3} \)cm
D). 4 cm
-- View Answer


6). The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle?
A). \( \Large 6cm^{2} \)
B). \( \Large 8cm^{2} \)
C). \( \Large 10cm^{2} \)
D). \( \Large 12cm^{2} \)
-- View Answer
7). If the area of an equilateral triangle is x and its perimeter is y. then which one of the following is correct?
A). \( \Large y^{4}=432x^{2} \)
B). \( \Large y^{4}=216x^{2} \)
C). \( \Large y^{2}=432x^{2} \)
D). None of these
-- View Answer
8). The area of an isosceles \( \Large \triangle ABC \) with AB = AC and altitude AD = 3 cm is 12 sq cm. What is its perimeter?
A). 18 cm
B). 16 cm
C). 14 cm
D). 12 cm
-- View Answer
9). The area of an equilateral triangle is \( \Large \Large \frac{\sqrt{243}}{4} \)sq cm. Find the length of its side.
A). 3 cm
B). \( \Large 3\sqrt{3} \)cm
C). 9 cm
D). \( \Large \sqrt{3} \)cm
-- View Answer
10). The ratio of length of each equal side and the third side of an isosceles triangle is 3:4. If the area of the triangle is \( \Large \Large 18\sqrt{5} \) sq units, the third side is
A). \( \Large 8\sqrt{2} \)units
B). 12 units
C). 16 units
D). \( \Large 5\sqrt{10} \)units
-- View Answer