Application of Heron's Formula to Quadrilaterals MCQs

Q1. A diagonal divides a quadrilateral field into two triangular halves: one with edges 13,14,15 m and the other with edges 15,20,25 m. Using Heron's formula on each, by how much does the larger half exceed the smaller?

• A.66 m^2
• B.234 m^2
• C.150 m^2
• D.84 m^2

Answer: A. 66 m^2

The problem states: 15 m; 25 m. What we must find: how much does the larger half exceed the smaller?. Key equation - Half 1 Heron area = 84. This is the equation that links the given quantities to the unknown (math, chapter 'Heron's Formula'). Plugging the values in: Half 1 Heron area = 84 → half 2 Heron area = 150 → difference = |84-150| = 66 m^2. Hence the answer is A) 66 m^2. Why the other options fail: option B) '234 m^2' is incorrect: The question asks the difference, not the sum; option C) '150 m^2' fails since Subtract the smaller half's area from the larger's; option D) '84 m^2' doesn't hold - Report the difference of the two halves.

Q2. Rectangle L=7, B=4. Area?

• A.28 cm^2
• B.22 cm^2
• C.11 cm^2
• D.29 cm^2

Answer: A. 28 cm^2

Diagnose the question type - a typical math numerical. The data on the table: 7, 4. We are after the quantity the stem asks for. Tool of choice - area = 28. Rearrange it for the unknown before substituting. Numbers in: area = 28. Lock in option A) 28 cm^2. Trap-watch: option B) '22 cm^2' is incorrect: Perimeter; option C) '11 cm^2' fails since Multiply.

Q3. Rectangle L=11, B=6. Area?

• A.66 cm^2
• B.34 cm^2
• C.17 cm^2
• D.67 cm^2

Answer: A. 66 cm^2

Reading off the stem: 11; 6. The unknown asked is: the unknown asked in the stem. Relation we use - area = 66. This is the equation that links the given quantities to the unknown (math, chapter 'Heron's Formula'). Numerically: area = 66. Hence the answer is A) 66 cm^2. The other choices: option B) '34 cm^2' doesn't hold - Perimeter; option C) '17 cm^2' misses the point - Multiply.