# Competency Based Questions Chapter 10 Heron’s Formula

Hint: Calculate area of a given triangle to state the limitation of the Standard formula (Area of Triangle = \frac{1}{2}\times b \times h).

Question.1. Two triangles are shown below.Which of following is true?

(a) Area of both the triangles can be calculated, area of ∆XYZ = 140 cm^{2} and area of ∆PQR = 180 cm^{2}
(b) Area of only triangle XYZ can be calculated, area of ∆XYZ = 140 cm^{2}
(c) Area of only triangle PQR can be calculated, area of ∆PQR = 180 cm^{2}
(d) Area of both the triangles cannot be calculated

Question.2. A figure is shown below.Can we find the area of the quadrilateral KLMN?

(a) No, as the side MK is unknown.
(b) No, as the side NK is unknown.
(c) Yes, and the area of the quadrilateral KLMN is 192 cm^{2}.
(d) Yes, and the area of the quadrilateral KLMN is 384 cm^{2}.

Ans.1. (c) Area of only triangle PQR can be calculated, area of ∆PQR = 180 cm^{2}
Ans.2. (c) Yes, and the area of the quadrilateral KLMN is 192 cm^{2}.

Hint: Apply Heron’s formula in order to calculate the area of a Triangle.

Question.3. A triangle is shown below.Which of following is equal to the area of the triangle?

(a) \sqrt{(9)(5)(1)}
(b) \sqrt{15(9)(5)(1)}
(c) \sqrt{(24)(20)(16)}
(d) \sqrt{30(24)(20)(16)}

Question.4. A triangle is shown below.If the perimeter of the triangle is 192 m, what is the length of AH?

(a) 38.4 m
(b) 40 m
(c) 76.8 m
(d) 80 m

Ans.3. (b) \sqrt{15(9)(5)(1)}
Ans.4. (a) 38.4 m

Hint: Breakdown a given polygon into triangles in order to find the area of a given polygon as a sum of areas of those triangles.

Question.5. A quadrilateral ABCD is shown below.Which is the area of ABCD?

(a) 61.94 cm^{2}
(b) 86.96 cm^{2}
(c) 123.88 cm^{2}
(d) 173.92 cm^{2}

Question.6. The sketch of a farm is shown below.What is the area of the farm?

(a) 1336.04 m^{2}
(b) 2140.04 m^{2}
(c) 2170.04 m^{2}
(d) 3004.04 m^{2}

Ans.5. (a) 61.94 cm^{2}
Ans.6. (c) 2170.04 m^{2}

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