In the given figure, PQR is a triangle whose area is 75 cm2. S and T are mid-points of sides PQ and PR respectively. Calculate the area of quadrilateral SQRT.

56.25 cm2 Reason Using midpoint theorem, which states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and is half the length of the third side. Given, S and T are the midpoints of PQ and PR. ST || QR and ST = Draw PM perpendicular to QR. Let PM meets ST at N. As, ST || QR ∴ ∠SNP = ∠QMN = 90° As, S is mid-point of PQ and SN || QM, ∴ N is mid-point of PM. Area of triangle = Area of trapezium STRQ = Area of △PQR - Area of △PST = 75 - 18.75 = 56.25 cm2.

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Mathematics

In the given figure, PQR is a triangle whose area is 75 cm². S and T are mid-points of sides PQ and PR respectively. Calculate the area of quadrilateral SQRT.

Mid-point Theorem

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Mathematics

In the given figure, PQR is a triangle whose area is 75 cm². S and T are mid-points of sides PQ and PR respectively. Calculate the area of quadrilateral SQRT.

Mid-point Theorem

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In △ABC, AB = AC. D, E and F are mid-points of the sides BC, CA and AB respectively. Show that :
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Mathematics

In the given figure, PQR is a triangle whose area is 75 cm2. S and T are mid-points of sides PQ and PR respectively. Calculate the area of quadrilateral SQRT.

Mid-point Theorem

Related Questions

In △ABC, AB = AC. D, E and F are mid-points of the sides BC, CA and AB respectively. Show that :(i) AD is perpendicular to FE.(ii) AD and FE bisect each other.

In the given figure, PQR is a triangle whose area is 75 cm². S and T are mid-points of sides PQ and PR respectively. Calculate the area of quadrilateral SQRT.

In △ABC, AB = AC. D, E and F are mid-points of the sides BC, CA and AB respectively. Show that :
(i) AD is perpendicular to FE.
(ii) AD and FE bisect each other.