In this giving figure ABCD is a quadrilateral with the given measurements . All the measurements are given in cm
1) Area of ∆ABC
2) Area of ∆ACD
3)Area of quadrilateral ABCD
Answers
Area of triangle ABC=1/2*b*h
=1/2*12*16
=96cm^2
Area of triangle ACD =√s(s-a)(s-b)(s-c)
We will use Herons Formula
Semi perime
✪SOLUTION✪
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★Given :
AB = 16 cm, BC = 12 cm
CA = 20 cm, Ad = 21 cm &
CD = 29 cm
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★To find :
1) Area of ∆ABC
2) Area of ∆ACD
3)Area of quadrilateral ABCD
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Let's solve,
★Area of Triangle ABC
We find the area of Traingle
ABC by using Heron's formula
So,
Firstly we find The semi - perimeter
⇒ S = AB + BC + CA ÷ 2
⇒ S = 16 + 12 + 20 ÷ 2
⇒ S = 48 ÷ 2
⇒ S = 24
∴ Area = √s (s-a) (s-b) (s-c)
⇒ A = √24 (24-16) (24-12) (24-20)
⇒ A = √ 24 × 8 × 12 × 4
⇒ A = √9216
⇒ A = 96 cm²
∴ Area of Triangle ABC = 96 cm²
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★Area of Triangle ACD
Here, we have to do same.
⇒ S = AC + CD + DA ÷ 2
⇒ S = 20 + 29 + 21 ÷ 2
⇒ S = 70 ÷ 2
⇒ S = 35
⇒ A = √35 (35-20) (35-29) (35-21)
⇒ A = √35 × 15 × 6 × 14
⇒ A = √44100
⇒ A = 210 cm²
∴ Area of Triangle ACD = 210 cm²
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★Area of Quad. ABCD
Area of quad. ABCD
= Area of ΔABC + Area of Δ ACD
= 96 + 210
= 306 cm²
∴ Area of quad. ABCD = 306 cm²
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Therefore,
1) Area of ∆ABC = 96 cm²
2) Area of ∆ACD = 210 cm²
3)Area of quadrilateral ABCD = 306 cm²
