7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 1\",\"description\":\"Area and volume fundamentals.\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-geometry-area-volume-quiz-1\",\"educationalLevel\":\"Fundamental\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Geometry and Trigonometry - Area and volume\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Quiz 1\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-geometry-area-volume-quiz-1\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","div",null,{"className":"container mx-auto px-4 py-8 md:py-12","children":[["$","div",null,{"className":"mb-12","children":["$undefined",["$","div",null,{"className":"mb-8","children":["$","h1",null,{"className":"text-4xl md:text-5xl lg:text-6xl font-bold text-gray-900 mb-4","children":"Quiz 1"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Area and volume fundamentals.

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Practice problems focused on area and volume concepts for PSAT 8/9.

"},"excerpt":{"rendered":"

Area and volume fundamentals.

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Fundamental","categorie":"Geometry and Trigonometry - Area and volume","nombre_questions":10,"score_minimum":90,"ordre_questions":"Fixe","questions":[{"id":"cmrk8f0kv0y94jg8wr2ft81p0","texte_question":"

What is the area, in square inches, of a rectangle with a length of $$9$$ inches and a width of $$5$$ inches?

","type_question":"QCM","explication":"

Use the formula for the area of a rectangle.

$$Area=length \\times width$$

Substitute $$9$$ for the length and $$5$$ for the width.

$$Area=9 \\times 5$$

Multiply.

$$Area=45$$

The area of the rectangle is $$45$$ square inches.

Final answer: $$45$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$14$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$45$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$18$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$90$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0ky0y9ajg8wpg2shdrz","texte_question":"

The area of a square is $$81$$ square inches. What is the side length, in inches, of this square?

","type_question":"QCM","explication":"

Use the formula for the area of a square.

$$Area=s^2$$

The area is $$81$$.

$$s^2=81$$

Take the square root of both sides.

$$s=\\sqrt{81}$$

Simplify.

$$s=9$$

The side length of the square is $$9$$ inches.

Final answer: $$9$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$9$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$18$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$27$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$81$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0l10y9gjg8wpf0x9ht4","texte_question":"

The lengths of two sides of a triangle are $$5$$ centimeters and $$7$$ centimeters. If the perimeter of the triangle is $$20$$ centimeters, what is the length, in centimeters, of the third side?

","type_question":"QCM","explication":"

Use the formula for perimeter.

$$Perimeter=side_1+side_2+side_3$$

Substitute the known values.

$$20=5+7+x$$

Add the known side lengths.

$$20=12+x$$

Subtract $$12$$ from both sides.

$$x=8$$

The third side is $$8$$ centimeters.

Final answer: $$8$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$8$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$6$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$12$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$20$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0l40y9mjg8wx2qo57nr","texte_question":"

A rectangle has a length of $$15$$ and a width of $$4$$. What is the perimeter of the rectangle?

","type_question":"QCM","explication":"

Use the formula for the perimeter of a rectangle.

$$P=2(l+w)$$

Substitute $$15$$ for the length and $$4$$ for the width.

$$P=2(15+4)$$

Add inside the parentheses.

$$P=2(19)$$

Multiply.

$$P=38$$

The perimeter of the rectangle is $$38$$.

Final answer: $$38$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$19$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$38$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$60$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$30$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0l70y9sjg8wdrwkfekq","texte_question":"

What is the area of a rectangle with a length of $$12$$ centimeters and a width of $$9$$ centimeters?

","type_question":"QCM","explication":"

Use the formula for the area of a rectangle.

$$Area=length \\times width$$

Substitute $$12$$ for the length and $$9$$ for the width.

$$Area=12 \\times 9$$

Multiply.

$$Area=108$$

The area of the rectangle is $$108$$ square centimeters.

Final answer: $$108cm^2$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$21cm^2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$54cm^2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$108cm^2$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$216cm^2$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0la0y9yjg8wan73vmxm","texte_question":"

What is the area of a rectangle with a length of $$6$$ centimeters and a width of $$3$$ centimeters?

","type_question":"QCM","explication":"

Use the formula for the area of a rectangle.

$$Area=length \\times width$$

Substitute $$6$$ for the length and $$3$$ for the width.

$$Area=6 \\times 3$$

Multiply.

$$Area=18$$

The area of the rectangle is $$18$$ square centimeters.

Final answer: $$18cm^2$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$9cm^2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$18cm^2$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$27cm^2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$36cm^2$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0ld0ya4jg8w1uwsvzm7","texte_question":"

What is the area, in square feet, of a triangle with a base of $$10$$ feet and a height of $$6$$ feet?

","type_question":"QCM","explication":"

Use the formula for the area of a triangle.

$$Area=\\frac{1}{2}bh$$

Substitute $$10$$ for the base and $$6$$ for the height.

$$Area=\\frac{1}{2}(10)(6)$$

Multiply.

$$Area=\\frac{1}{2}(60)$$

Simplify.

$$Area=30$$

The area of the triangle is $$30$$ square feet.

Final answer: $$30$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$16$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$30$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$60$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$120$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0lf0yaajg8wi15r36i8","texte_question":"

A cube has a side length of $$4$$ inches. What is the volume of the cube, in cubic inches?

","type_question":"QCM","explication":"

Use the formula for the volume of a cube.

$$V=s^3$$

Substitute $$4$$ for the side length.

$$V=4^3$$

Evaluate the exponent.

$$V=4 \\times 4 \\times 4$$

$$V=64$$

The volume of the cube is $$64$$ cubic inches.

Final answer: $$64$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$16$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$32$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$48$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$64$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0li0yagjg8wcpnwutev","texte_question":"$18","type_question":"QCM","explication":"

Use the formula for the volume of a rectangular prism.

$$V=lwh$$

Substitute $$6$$ for the length, $$2$$ for the width, and $$3$$ for the height.

$$V=6 \\times 2 \\times 3$$

Multiply.

$$V=12 \\times 3$$

$$V=36$$

The volume of the prism is $$36$$ cubic centimeters.

Final answer: $$36$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$36$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$24$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$12$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$11$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0lp0yamjg8wfxf3ufed","texte_question":"

A rectangular box has a volume of $$96$$ cubic inches. Its length is $$8$$ inches and its width is $$3$$ inches. What is the height, in inches, of the box?

","type_question":"QCM","explication":"

Use the formula for the volume of a rectangular prism.

$$V=lwh$$

Substitute $$96$$ for the volume, $$8$$ for the length, and $$3$$ for the width.

$$96=8 \\times 3 \\times h$$

Multiply $$8$$ and $$3$$.

$$96=24h$$

Divide both sides by $$24$$.

$$h=4$$

The height of the box is $$4$$ inches.

Final answer: $$4$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$3$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$4$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$6$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["geometry-and-trigonometry-area-and-volume"],"date":"2026-06-04T09:04:49.273Z","modified":"2026-07-14T05:49:54.218Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L19",null,{"targetType":"quiz","targetSlug":"psat-8-9-geometry-area-volume-quiz-1"}]}]]}]}]]

Quiz 1

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