Given:

Question

LM
 ∥ 
KN
 ,
KL
 ∥ 
NM
 
       LP = h­1 = 5 cm, MQ = h2 = 6 cm
       PKLMN = 42 cm
       Find: Area of KLMN

Steve · Answer

What purpose does Q serve?

Explain Bot · Answer

To find the area of quadrilateral KLMN, we can divide it into two triangles (KLM and NML) and then sum the areas of the two triangles. Step 1: Find the length of KL and NM Since KL is parallel to NM, we can use the given information to find the lengths of KL and NM. Since LP and MQ are the heights of the trapezoids LKMP and MQNP, respectively, we can say that h₁ = LP = 5 cm and h₂ = MQ = 6 cm. To find KL, we can use the similar triangles LKM and LNP. The corresponding sides of similar triangles are proportional. KL / LM = LP / LN KL / (KL + LM) = h₁ / (h₁ + h₂) KL / (KL + 42) = 5 / (5 + 6) KL / (KL + 42) = 5 / 11 Cross-multiplying, we have: 11KL = 5(KL + 42) 11KL = 5KL + 210 6KL = 210 KL = 35 cm Similarly, we can find NM using similar triangles KMN and LNP. NM / LM = LN / LP NM / (NM + 42) = h₁ / (h₁ + h₂) NM / (NM + 42) = 5 /11 Cross-multiplying, we have: 11NM = 5(NM + 42) 11NM = 5NM + 210 6NM = 210 NM = 35 cm Therefore, we have KL = 35 cm and NM = 35 cm. Step 2: Calculate the area of triangle KLM We can use the formula for the area of a triangle to find the area of triangle KLM. Area of triangle KLM = (1/2) * base * height = (1/2) * KL * LM = (1/2) * 35 cm * 42 cm = 735 cm² Step 3: Calculate the area of triangle NML We can use the formula for the area of a triangle to find the area of triangle NML. Area of triangle NML = (1/2) * base * height = (1/2) * NM * LM = (1/2) * 35 cm * 42 cm = 735 cm² Step 4: Calculate the area of quadrilateral KLMN Since KLMN is the combination of triangles KLM and NML, we can find its area by summing the areas of the two triangles. Area of quadrilateral KLMN = Area of triangle KLM + Area of triangle NML = 735 cm² + 735 cm² = 1470 cm² Therefore, the area of quadrilateral KLMN is 1470 cm².

A-343479 · Answer

Given: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMNGiven: LM ∥ KN , KL ∥ NM LP = h­1 = 5 cm, MQ = h2 = 6 cm PKLMN = 42 cm Find: Area of KLMN