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P is Any Point on Base Bc of δAbc and D is the Mid-point of Bc. De is Drawn Parallel to Pa to Meet Ac at E. If Ar (δAbc) = 12 Cm2, Then Find Area of δEpc. - Mathematics

Answer in Brief

P is any point on base BC of ΔABC and D is the mid-point of BCDE is drawn parallel toPA to meet AC at E. If ar (ΔABC) = 12 cm2, then find area of ΔEPC

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Solution

Given: Area (ABC) = 12 cm2, D is midpoint of BC and AP is parallel to ED. We need to find area of the triangle EPC. 

Since, AP||ED, and we know that the area of triangles between the same parallel and on the same base are equal. So,

Area (APE) = Area (APD)

⇒ Area (APM) + Area (AME) = Area (APM) + Area (PMD)

⇒ Area (AME) = Area (PMD) …… (1)

Since, median divide triangles into two equal parts. So,

Area (ADC) = `1/2` Area (ABC) = `12/2`  = 6 cm2

⇒ Area (ADC) = Area (MDCE) + Area (AME)

Area (ADC) = Area (MDCE) + Area (PMD) (from equation (1))

⇒ Area (ADC) = Area (PEC)

Therefore,

Area (PEC) = 6 cm2.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 10 | Page 60
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